text:
Coronavirus stimulus plan could deliver $3K to family of four
Mnuchin said the first round of checks would be sent within three weeks of enactment
Senate Majority Leader Mitch McConnell, R-Ky., waits in a subway cart in the Senate subway in between votes in the Capitol in Washington on Wednesday. (Photo by Caroline Brehman/CQ Roll)
By David Lerman
Posted March 19, 2020 at 9:29am
The emerging $1 trillion aid package intended to help weather the COVID-19 economic storm appears likely to deliver $1,000 to every U.S. adult, plus $500 per child, according to Treasury Secretary Steven Mnuchin and a GOP senator involved in the drafting.
"So for a family of four, that's a $3,000 payment," Mnuchin told Fox Business on Thursday morning, adding that he thinks the checks would be sent within three weeks of enactment.
"That may change in negotiations with Democrats, but that's the priority right now," GOP Sen. Mitt Romney of Utah said on the Hugh Hewitt radio show, confirming the basic structure of the plan under discussion.
Mnuchin said a second round of checks in the same amount would go out six weeks later if economic conditions haven't improved and the "national emergency" Trump declared last week is still in effect. Mnuchin said most households wouldn't have to worry about venturing to the bank to cash their checks and risk virus exposure: "It's really money direct-deposited, most people."
Those comments came as Senate Republicans continued to draft stimulus legislation that some lawmakers have said could get a floor vote as early as this weekend. "We're working with Democrats and Republicans and there's a lot of goodwill going on," President Donald Trump said at a White House news conference Thursday.
The stimulus checks were expected to cost roughly $500 billion, under an outline prepared by the Treasury Department, accounting for about half the cost of the aid package. The remainder would be a $300 billion small-business lending program, and $200 billion in loans and loan guarantees for "severely distressed" industries, with airlines in line for a $50 billion slice of that provided they adhere to certain restrictions, including on executive compensation.
Senate Majority Leader Mitch McConnell, R-Ky., outlined the major elements of the bill Republicans are drafting, including expanded federal relief to small businesses. "We're talking about new federally guaranteed loans on the order of hundreds of billions of dollars to address immediate cash-flow problems," he said in a floor speech.
McConnell also endorsed the proposed cash payments to individuals, saying, "It's not an ordinary policy, but this is no ordinary time." And he called for "targeting lending to industries of national importance," such as the airlines, while stressing that any loans would have to be repaid.
Senate Minority Leader Charles E. Schumer, D-N.Y., said any effort to shore up struggling industries must help "workers first." He said Democrats want to ensure that employees are protected in any potential bailout of companies by prohibiting corporations from buying back stock, rewarding executives or laying off workers.
Trump suggested he would be willing to accept such conditions, while noting there are many people involved in drafting the bill. "It takes many, many people in this case to tango," he said at the White House.
But the size of any stimulus checks to families could become a sticking point when Republicans present their draft plan to Democrats for negotiation. Schumer said any cash payments to individuals need to be "bigger, more generous and more frequent" than some of the GOP proposals he's seen.
[Redefining district work: House members opt to telework during coronavirus pandemic]
And he said those cash payments cannot be a substitute for the other Democratic priorities, including expanded paid leave and unemployment insurance for workers. "The pandemic requires bold, structural changes to our society safety net to give people a lifeline for months, not just weeks," Schumer said.
Mnuchin and Romney said the small-business loan plan would include debt forgiveness for firms that keep people employed throughout the crisis.
Romney said the industry-specific credit facility will be "a great deal larger than just what's needed for airlines." He added that "it'll be for those enterprises that are larger that are in difficult circumstances. How many will qualify is a real question. But those enterprises that are really key to the economy, key to national security, key to our infrastructure, will surely be high on the list."
Romney also suggested the package could aid hospitals struggling with a surge in patients and a loss in revenue. He said the Senate Health, Education, Labor and Pensions Committee is focused on making sure hospitals have enough face masks, test kits and the like.
"We've got a lot of hospitals that are closing down their elective surgeries. That's where they make their money," Romney said. "They're opening the doors to COVID-19 patients. So getting help there is the highest priority."
Democratic support needed
While the discussions have been among Senate Republicans and the White House for the most part thus far, Mnuchin has also held talks with Schumer and Speaker Nancy Pelosi, D-Calif. Votes from Schumer's caucus will be needed to get over the Senate's 60-vote threshold, given Republicans number only 53 in that chamber and there could be GOP defections over what some might term a costly bailout.
Schumer told CNN on Wednesday night that when he spoke with Mnuchin he told him workers needed to come first before aid was delivered directly to employers.
"If there are going to be some of these corporate bailouts, we need to make sure workers and labor come first. That people are not laid off. That people's salaries are not cut," Schumer said.
He also suggested corporate stock buybacks should be limited in some form, pointing specifically to reports that U.S. airlines had repurchased $45 billion of their own shares over the last decade — nearly equaling the new aid package sought by the industry. When companies buy back shares, the money isn't available for hiring or investment in plant and equipment, though it drives up earnings per share and rewards shareholders.
The House, meanwhile, is in recess this week but was expected to return as soon as a Senate bill is passed. "The House will not return to session until we are in a position to vote on the third piece of emergency legislation to respond to the economic impact of this crisis," House Majority Leader Steny H. Hoyer, D-Md., said in a "Dear Colleague" letter Thursday.
Hoyer said the House will adjust its voting procedures to follow the Centers for Disease Control and Prevention's recommendations for social distancing but that no decisions have been made on exactly what those changes will be. "We will be discussing all options," he said.
Sen. Benjamin L. Cardin, D-Md., told CQ Roll Call on Wednesday night that the small business lending provisions had more bipartisan support than other pieces under discussion.
"We've had conversations about it," Cardin said. "I think many Republican senators realize that we really need to put our nation first, and it would be a major mistake to just come out with a partisan proposal. … There should be conversations."
Romney said those conversations will happen, it's just a matter of when.
"You've heard the expression in the law which is the wheels of justice grind slowly. Well, the wheels of Congress grind even slower. And so Mitch has cut through all this by organizing task forces to draft a package for review," he told Hewitt. "And that's record speed for this institution. Now, of course, we've got to deal with our Democrat friends and see what they want to do and compromise and make something happen."
As soon as the stimulus measure is passed, McConnell said, the Senate would turn to an emergency White House appropriations request "so we can keep funding health care and other priorities." The White House submitted a request for nearly $46 billion this week to fund programs in the Department of Health and Human Services, the Department of Veterans Affairs and other agencies.
But Democrats have already criticized the White House request as insufficient and Senate Appropriations Chairman Richard C. Shelby, R-Ala., suggested Thursday the measure the Senate takes up would be bigger. When asked if McConnell was referring strictly to the White House request, Shelby said, " "It's referring to a lot of stuff that we might have to pick up. We're thinking of a 4th [stimulus] package."
Niels Lesniewski, Jennifer Shutt and Paul M. Krawzak contributed to this report.


We've recently gotten a few inquiries from business owners that are completely overwhelmed by managing their businesses' social media accounts. They just don't know where to start when it comes to tackling all of the notifications from Facebook and then dealing with entirely different platform letting them know that they have 10 more new notifications over on it On top of all that, they have to think about creating the content that goes out on to these platforms. We get it, it can be a lot. And you might be starting to feel like Kevin, From The Office every time you try to tackle it.
As a social media management agency, our first instinct is to reach out and take the stress of social media off of your plate. Let you focus on the things you do best. However, we understand that that's not what every business owner wants. A lot of you want to remain in control and test the waters for yourself first. So, for those of you out there who still want to tackle all things social in-house, we've put together a few tips for you that may help.
The idea of creating a strategy for your business' social media marketing might be another one of those things you find overwhelming, but it's necessary for your success. We recommend starting small. Figure out how much time a week you can spend on content creation and social media management. Then during those specific times, nail down the tone you want to be using in your posts (i.e. humours, serious, etc.), the message you want to get across to your followers, and how you envision spreading that message (i.e. videos, photos, etc.). Content calendars can be a huge help when you are getting started so try creating one of those to help you lay out your plans. Once you define your goals, you'll have a much easier time creating a strategy that helps you reach them.
There are a lot of tools out there, specifically for social media use, that have been created to help save you time. While we always want to encourage you to post natively to the platform if possible (Facebook does, in fact, have a built-in post scheduler)! We know that posting natively to each platform is not always an option because, hello you have other things to do. Tools like Buffer and Hootsuite are great examples of scheduling software that you can use for free. They do have monthly subscription based plans, should you want some of the features from one of their premium options, but we have found that most of our clients who need to use a scheduling software have all gotten away with using the free version.
If you've kept up with our blog over the last little while, you might be thinking that we are starting to sound like a broken record. But we cannot stress enough how important it is for you to be authentic on social media. If you aren't already posting visuals that include the friendly faces of your staff, or you as the business owner, give it a try. We guarantee that you will notice a huge increase in your engagement with those kinds of posts.
Now some of you may be wondering, "Well how do I know when my posts have an increase in engagement?". On social media platforms, like Facebook and Instagram, there are business account versions that actually have free built-in analytics. These analytics and insights help you to determine and analyze things like the best times to post, what kinds of posts your audience likes best, and how many people you are reaching on a daily basis. The insights tab for Facebook can be found in the top row of tabs when you are looking at your business page on a desktop.
You can also use apps like FacebookPage and Facebook Ads to manage your accounts on a mobile device. It's so important to keep track of the analytics behind your page. By measuring your success and the engagement of your audiences, you will have a much better understanding of what works and what doesn't work for your followers.
When you set out to post something on Facebook, or share a photo to Instagram, think about why you are doing so in the first place. It might help to ask yourself a few questions like, "If I saw this on my feed would I like it?", or "Is this providing some form of value to my audience?". If the answer isn't yes to either of those questions, you might want to reconsider your post. If you are just posting for the sake of putting out content, then quite frankly you are doing it wrong.
If you try out any of these tips over the next few weeks, let us know in the comments below. Also, if you have any other tips or suggestions for small business owners that we haven't touched on here we would love to hear them. Sharing is caring!
© 2019 XXIV Social. All rights reserved.


text:
Women and agricultural productivity: what does the evidence tell us?
Authors: Doss, C.
Content type: Bulletin
Should agricultural development programs target women in order to increase productivity? This paper reviews the extensive literature on men's and wome...
Gender, livestock and reducing greenhouse gas emissions in Costa Rica.
Published online: 20 Jan 2016
Authors: Farnworth, C. R.
Costa Rica is developing a Nationally Appropriate Mitigation Action (NAMA) that will provide climate finance for best livestock management practices t...
Background paper on gender implications of the GAP and KJWA: AGNES pre-SBs 50 strategy meeting on agriculture and food security.
Authors: Masiko, W. K. & Huyer, S. & Mungai, C.
In Africa, women play an important role in food production, both paid and unpaid, and use of natural resources, while also serving as key figures in c...
Under the canopy: gender and forests in Amazonia.
Authors: Schmink, M. & Gómez-García, M. A.
Despite the importance of forests for global processes and the tradition of forest management by local Amazonian peoples, there is not much available ...
Linking social protection and water security to empower women and girls.
Authors: Lowe, C. & Ludi, E. & Seve, M. D. le & Tsui, J.
Water insecurity is a significant, heavily gendered, and growing driver of poverty, vulnerability and risk. This paper explores the linkages between t...
Design climate-smart agricultural interventions to be gender inclusive.
Authors: Twyman, J. & Mwongera, C. & Läderach, P. & Acosta, M. & Ampaire, E. & Eitzinger, A. & Lamanna, C. & Mwungu, C. & Shikuku, K. & Winowiecki, L.
Research suggests that gender equity is a critical factor in the adoption of climate-smart agricultural (CSA) practices. If gender is not explicitly c...
Women's empowerment and crop diversification in Bangladesh: a possible pathway to climate change adaptation and better nutrition.
Authors: Pinto, A. de & Seymour, G. & Bryan, E. & Bhandari, P.
The existing literature shows that climate change will likely affect several of the dimensions that determine people's food security status in Banglad...
How resilient are farming households, communities, men and women to a changing climate in Africa?
Authors: Pérez, C. & Jones, E. & Kristjanson, P. & Cramer, L. & Thornton, P. & Förch, W. & Barahona, C.
Social, economic and institutional factors and driving forces enhance or hinder the adaptation capacity of agricultural and pastoral households and co...
A framework to understand gender and structural vulnerability to climate change in the Ganges River Basin: lessons from Bangladesh, India and Nepal.
Authors: Sugden, F. & Silva, S. de & Clement, F. & Maskey-Amatya, N. & Vidya Ramesh & Anil Philip & Bharati, L.
This review presents a framework for understanding structural vulnerability to climate change in the Ganges River Basin countries: Nepal, India and Ba...
How do people see nature? Perceptions of naturalness in designed urban green spaces.
Authors: Hoyle, H. & Jorgensen, A. & Hitchmough, J.
This paper presents the results of surveys conducted to determine the perceptions of people to varying degrees of naturalness in designed urban green ...

redpajama_set_name: RedPajamaCommonCrawl


text:
Home > SPJ News > Society of Professional Journalists names Ron Sylvester Regional Director of the Year
Society of Professional Journalists names Ron Sylvester Regional Director of the Year
WASHINGTON, D.C. -- The Society of Professional Journalists, one of the nation's largest and most broad-based journalism-advocacy organizations, is pleased to honor Wichita Eagle reporter Ron Sylvester with its annual Regional Director of the Year Award.
Sylvester is the director of Region 7, which includes oversight of SPJ chapters in Iowa, Kansas, Missouri and Nebraska. He is the second generation from his family to belong to SPJ. His father, a broadcast pioneer from Missouri, joined SPJ when it was the Sigma Delta Chi fraternity in 1950. After visiting his father on the job and hearing the clacking of teletype machines, Sylvester ended up working for his hometown newspaper, the Springfield News-Leader, for 24 years. His first assignment was women's athletics, which he was the first reporter at the paper to cover the beat.
After being asked to leave college because he devoted more time to the newspaper than to classes, Sylvester continued to work in journalism, covering every beat in the newsroom, including arts and entertainment, public health, medicine, science and technology. He even found time to write a book on the development of Branson, Mo., as an entertainment tourist destination. Today, Sylvester covers legal affairs for the Wichita Eagle and works as a stringer for Court TV. Today, Sylvester says he cannot think of a better way to make a living.
According to Immediate Past President Christine Tatum, Sylvester received the Regional Director of the Year award because of his dedication to furthering the journalism field and his abilities to help journalists and citizens understand why newsgathering plays an important role in shaping communities.
"I salute Ron Sylvester for serving as a great example of where journalists — many of whom are struggling to navigate a news industry plagued with turmoil and uncertainty — should be heading," Tatum said. "Ron has invited everyone — not just SPJ members in his region — to learn alongside him, to collaborate with him and to contribute to the big-idea discussions he facilitates through SPJ's 'Technolo-J' blog.
"Ron is also an exceptional regional director because he innovates and isn't afraid to push SPJ into new territory that helps the Society retain members and continue its profoundly important work."
Each year, SPJ honors an outstanding regional director for exceptional service and contributions to their region and the Society during the preceding year. Nominations for the award may be made by chapters or members. Sylvester was honored at a dinner Saturday, Oct. 6, during the 2007 SPJ Convention & National Journalism Conference in Washington, D.C.
Founded in 1909 as Sigma Delta Chi, SPJ promotes the free flow of information vital to a well informed citizenry; works to inspire and educate the next generation of journalists; and protects First Amendment guarantees of freedom of speech and press. For more information about SPJ, please visit www.spj.org.


business management and leading a company or organization.
Leadership books are listed alphabetically by the author's last name.
The flamboyant Virgin entrepreneur from the United Kingdom shares some of his business successes, world adventures, and personal background in his bubbly autobiography. "Losing My Virginity: How I've Survived, Had Fun, and Made a Fortune Doing Business My Way" is a very appropriate title as it is exactly what the book is about.
Jennifer Prosek's "Army of Entrepreneurs" book is a practical guide to growing your business through inspiring and empowering your employees. Prosek shares how she turned her company around and gives real world examples of how you can too.
"Jack: Straight from the Gut" is written by one of the most well known American business leaders of recent times. Jack Welch played a leading role in one of America's largest companies (General Electric - GE) for twenty years, growing it from around $26 billion when he started through to $130 billion when he left in 2001.
If you have read one of the Leadership books listed above, please share your thoughts on it. Let other know if it was worth reading or should have been left sitting on the book shelf!


text:
Type Investigations Announces the 2020 Ida B. Wells Fellows
by Type Investigations
The fellows represent a cross-section of the U.S. and of journalism experience, ranging from emerging to mid-career journalists. Each fellow will be given the opportunity to complete their first substantial piece of investigative reporting, receiving a $16,000 stipend, plus funds to cover reporting costs in addition to intensive editorial feedback, legal counsel, research resources, mentoring, and assistance with story placement and publicity.
"The disparate impact of COVID-19 on minority communities shows how crucial it is to have reporters of color pursuing ambitious investigative stories. Now, as much as ever, we must empower and support journalists from underrepresented groups in telling the stories that matter most to their communities," said Alissa Figueroa, senior editor in charge of the Ida B. Wells Fellowship Program.
People of color constitute less than 23 percent of all newsroom jobs, according to the most recent annual survey by the American Society of Newsroom Editors, and 19 percent of supervisors; their presence is even smaller on investigative teams. Women are also underrepresented, holding only 42 percent of newsroom jobs. Survey data indicates that fewer than 10 percent of journalists come from a working-class background.
The Ida B. Wells Fellowship competition, now in its fifth year, is held annually. For the first time, we have selected a Southern Ida B. Wells Fellow based in a nine-state region in the south, where Ida B. Wells is from and where her anti-lynching reporting was based.
The fellowship program is made possible by Open Society Foundations, Foundation for a Just Society and the Schwab Charitable Fund, made possible by the generosity of the Present Progressive Fund. The Ida B. Wells Fellowship is a one-time educational opportunity and is non-renewable.
Tina Vasquez, our Southern Fellow, is a North Carolina-based movement journalist with more than 10 years of experience reporting on immigration, reproductive injustice, LGBTQ+ issues, and gender-based violence. She is currently a staff reporter leading Prism's coverage of gender justice. Previously, she was a senior reporter covering immigration at Rewire.News, the leading online publication devoted to evidence-based reporting on reproductive and sexual health, rights, and justice. Her work has appeared in the New York Review of Books, NPR, The Nation, Playboy, and a variety of other publications. Recently, she was a mentor in the Freedomways Fellowship Program as part of Press On, a Southern journalism collective that strengthens and expands the practice of journalism in service of liberation. She will be reporting on immigration in North Carolina.
Akintunde Ahmad is a Bay Area based multimedia journalist focusing on the intersection of education, economic inequality, and the justice system. Ahmad, an Oakland native, was most recently a Delacorte Fellow with the Columbia Journalism Review, where he wrote about news media and its influence on public perceptions. He holds a BA in sociology from Yale University and an MS in journalism and documentary film from Columbia University. His work has been featured in The Atlantic, The Appeal, Huffington Post, and MTV. He will be reporting on police.
Eileen Guo is an independent journalist who focuses on inequality and the unintended consequences of globalization. Based in Los Angeles, she has reported from across the United States, Afghanistan, Guatemala, Mexico, and China for outlets including The New York Times, National Geographic, Wired, Mother Jones, and NPR. She will be investigating novel uses of surveillance devices.
Jack Herrera is an independent reporter based out of San Francisco. He covers immigration, refugees, and Latino issues. His work has appeared in Politico Magazine, The Nation, Columbia Journalism Review, Popular Science, and elsewhere. In 2018, he covered the arrival of the two most prominent Central American "caravans" on-the-ground in Tijuana as a reporter for Pacific Standard. In spring of 2020, he began covering the coronavirus pandemic's effects inside ICE detention centers. He will be reporting on healthcare and immigration.
Irene Romulo is a journalist based in Cicero, Illinois, where she helps run Cicero Independiente, a bilingual news organization she co-founded. Her work centers on immigrants, Spanish-speakers, and organizing efforts. She is a proud City Bureau Reporting Fellowship alum and was a 2020 Voqal Fellow. She will be reporting on school discipline.
Type Investigations' mission is to produce high-impact investigative reporting that holds the powerful accountable.


SQL Server Integration Services (SSIS) has become the defacto standard for moving data in Microsoft shops. Although moving data is generally possible with the data flow components, sometimes scripting is necessary to address particular requirements. Unfortunately, SSIS Script Components can be complex and unlike typical .NET projects in Visual Studio have limitations due to architectural differences. Overcoming these obstacles can be time consuming and error prone. It's not uncommon for developers to make use of third party libraries, APIs, and Web Services in their applications or scripts. Doing so in SQL Server Integration Services poses some challenges and limitations. Moreover, some data transformations require asynchronous processing of data which are otherwise unachievable through a synchronous serial process.
We will also learn about a solution from Melissa on how to ease your SQL Server data management directly in Integration Services.
Meelad Vahdat is a Sales Engineer at Melissa Global Intelligence.


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Dev Watch
Analysts Keep Saying Big Data Is So Over
Tech analysts keep saying this Big Data thing is over, meaningless, but is anyone listening?
The cries to move on are getting almost plaintive. "Join us in the revolution!" said Forrester Research analyst Brian Hopkins last week in calling for followers to forget Big Data and turn to an alternative approach he developed with fellow analyst Ted Schadler.
First introduced in April, it's called systems of insight, and it has to deal with the ability to actually derive and act upon business insights gleaned from analysis of data. Join the systems of insight camp and you'll beat those Jurassic Big Data boys.
"Ted and I agree that this trend is only just starting and the impact will be huge," Hopkins wrote in a blog post titled "'Big Data' Has Lost Its Zing -- Businesses Want Insight And Action" last week. "Insights masters who get this are going to spank firms that cling to Big Data and the 'data driven' mantra. Guarantee it."
Well, everybody wants zing, and nobody wants to get spanked by competitors, so supporters of the new movement are weighing in on Twitter with the Forrester-supplied hashtags #SystemsOfInsight and #InsightsToExecution.
[Click on image for larger view.] Systems of Insight (source: Forrester Research)
But, plaintive or not, the Forrester cries for change aren't resonating alone in the "Something Data" wilderness. Several analysts and experts told me Big Data was over last year.
Gartner analyst Donald Feinberg said he doesn't even like to use the term "Big Data."
"'Big Data' is going to disappear in the next two or three years and it's going to be called -- guess what? -- 'data,'" Feinberg told me. "Once every vendor has a Big Data something, it no longer gives me a way to distinguish one vendor from another."
David Torres, senior director of Data & Analytics at Avanade, which provides Microsoft-focused consulting services, echoed similar thoughts. "Beyond Big Data, it's really, in my opinion, it's all data," he said. "You need to have a strategy for all your data."
The nascent Big Data strategy, though perhaps just in the famed "trough of disillusionment" of the Gartner hype cycle, does seem to be letting organizations down, according to recent research.
Just a week after a report from Gartner found that investment in Hadoop-based Big Data technologies "remains tentative" with poor adoption rates, a recent survey from Software AG identified "a Big Data paralysis" that's keeping enterprises from realizing the promised benefits of the analytics craze.
"Despite substantial hype and reported successes for early adopters, over half of respondents (54 percent) report no plans to invest at this time," the Gartner report stated. "Additionally, only 18 percent have plans to invest in Hadoop over the next two years."
"Challenges are holding organizations back from making the improvements that they need," the Software AG survey report said. "The majority of those surveyed report that their organization finds analyzing large amounts of data (73 percent) and acting on data in real-time (65 percent) as very real obstacles."
It's those exact challenges that Forrester analysts Hopkins and Schadler are trying to help enterprises overcome with their new systems of insight approach.
"Big Data isn't what it used to be," Hopkins said. "Not because firms are disillusioned with the technology, but rather because the term is no longer helpful." Companies have bought into the idea of big-scale analytics, he said, but that hasn't helped much in overcoming the challenges in using that analysis to support business decisions.
"Systems of insight are the business discipline and technology to harness insights and turn data into action," Hopkins said. "Systems of insight deliver what Big Data cannot -- effective action through insights-driven software; after all, that's the only thing firms really care about."
Hmm, "systems of insight." You know, I think that term has some real zing.
Posted by David Ramel on 07/01/2015 at 11:30 AM


Search Results for "plasma ball"
Plasma Ball or Lamp. Closeup.
Plasma Ball And Lightning in Slow Motion 240 fps. High voltage. Tesla generator. Close-up view of plasma ball with moving energy rays inside on black background. Electric ball on the black background.
A plasma globe or plasma lamp (also called plasma ball, dome, sphere, tube or orb, depending on shape) is (usually) a clear glass sphere filled with a mixture of various noble gases with a high-voltage electrode in the center of the sphere.
Plasma ball in copernic museum.
Close up slow panning shot across plasma ball in black room.
A giant plasma ball at a science center.


It's been three days now, I can't find the remote. The trips to the TV are beginning to wear me out. Last night alone, I was sentenced to watching comedians that are not funny any more because I am tired of those trips to the TV.
I have turned everything in the house upside down, inside out, but the remote seems to have mastered its hide and seek skills, I wish it was a phone; I would just call it and find it.
Thinking of what I can do to save this situation, my mind wonders and I catch myself pondering on the things whose value I realized only after I had lost them.
It never occurred to me that a matchbox held the future of my supper in its hands until one day when I came back home with pangs of hunger, dashed to the kitchen; gas was there, the tomatoes and onions were there, the spaghetti was ready to be cooked-only to look for the match box in vain and to make matters worse, the shops in the neighborhood were closed.
Then, I remembered the night when the "askari" almost shot me because he thought I was a thief breaking into my house – I had forgotten my keys at office- office was closed, home was closed- my phone battery was dead. I slept on the veranda only to be greeted with judgmental looks at office the following morning when I appeared at office in the same clothes looking haggard.
When I received a phone call that one of my friends was dead, I was grieved but most of all, I was guilty, this was October of another year but I had not replied to his Christmas Facebook message- how could I have known that was going to be his last Christmas?
Even though I have not found the remote yet, I thank God for the days I had it and above all that its disappearance has reminded me of the valuable lesson of treasuring the things I have when I still have them.


text:
#ifndef SAMPLE_ASSET_H
#define SAMPLE_ASSET_H

#include "FrameworkFoundation.h"

namespace SampleFramework
{

	class SampleAsset
	{
		friend class SampleAssetManager;
	public:
		enum Type
		{
			ASSET_MATERIAL = 0,
			ASSET_TEXTURE,
			ASSET_INPUT,

			NUM_TYPES
		}_Type;

		virtual bool isOk(void) const = 0;

		Type        getType(void) const { return m_type; }
		const char *getPath(void) const { return m_path; }

	protected:
		SampleAsset(Type type, const char *path);
		virtual ~SampleAsset(void);

		virtual void release(void) { delete this; }

	private:
		SampleAsset &operator=(const SampleAsset&) { return *this; }

		const Type m_type;
		char      *m_path;
		PxU32      m_numUsers;
	};

} // namespace SampleFramework

#endif

redpajama_set_name: RedPajamaGithub


text:
\section{Introduction}

In this paper, we are concerned with the space of probability-measure-preserving (p.m.p.) actions of a countable group, elaborated in Kechris' monograph \cite{ke}.
Before stating our main result, let us briefly review some known results on the space of p.m.p.\ actions.

Throughout the paper, let $G$ be a countable group, and let $(X, \mu)$ be a non-atomic standard probability space unless otherwise stated.
Let $\mathrm{Aut}(X, \mu)$ be the group of all measure-preserving Borel automorphisms of $(X,\mu)$, where two of them are identified if they agree $\mu$-almost everywhere.
The \textit{weak topology} on $\mathrm{Aut}(X,\mu)$ is defined as the topology generated by the sets
\[\{\, R \in \mathrm{Aut}(X,\mu) \mid \mu(R(P) \bigtriangleup S(P)) < \varepsilon  \text{ for all } P \in \mathcal P \,\}\]
for $S\in \mathrm{Aut}(X, \mu)$, $\varepsilon >0$, and a finite Borel partition $\mathcal P$ of $X$.
It is known that $\mathrm{Aut}(X,\mu)$ is a Polish group with respect to the weak topology (\ci{\S 10 (A)}{ke}).

We mean by a \textit{p.m.p.}\ action of $G$ on $(X, \mu)$ a homomorphism from $G$ into $\mathrm{Aut}(X, \mu)$.
Let $A(G, X, \mu)$ denote the set of all p.m.p.\ actions of $G$ on $(X,\mu)$, and let $\mathit{FR}(G,X,\mu)$ denote the set of all essentially free p.m.p.\ actions of $G$ on $(X,\mu)$.
As being in \cite{ke}, the set $A(G,X,\mu)$ is naturally identified with the subspace of the product space $\prod_G\mathrm{Aut}(X,\mu)$ equipped with the product topology of the weak topology.
For $\alpha \in A(G,X,\mu)$ and $g\in G$, we write $g^\alpha = \alpha(g)$.
We say that two actions $\alpha,\beta \in A(G,X,\mu)$ are \textit{measure-conjugate} if there exists $R \in \mathrm{Aut}(X,\mu)$ such that $g^\alpha x = Rg^\beta R^{-1}x$ for all $g \in G$ and $\mu$-almost every $x \in X$.
We then write $\alpha = R\beta R^{-1}$.
For $\alpha \in A(G,X,\mu)$, let $[\alpha]_\mathit{MC}$ denote the set of all actions $\beta \in A(G,X,\mu)$ that are measure-conjugate to $\alpha$.

The space $A(G,X,\mu)$ reflects many analytic properties of the group $G$.
For example, for every infinite amenable group $G$ and for every $\alpha \in \mathit{FR}(G,X,\mu)$, the set $[\alpha]_\mathit{MC}$ is weakly dense in $A(G,X,\mu)$ (\ci{\S 3.1}{ag}; see also \ci{Remark, p.91}{ke}).
By contrast, every non-amenable group $G$ has an uncountable antichain in $\mathit{FR}(G,X,\mu)$ with respect to the pre-order of weak containment (\ci{Remark 4.3}{td}).
We say that $\alpha \in A(G,X,\mu)$ is \textit{weakly contained} in $\beta \in A(G,Y,\nu)$ (denoted by $\alpha \prec \beta$) if for any Borel subsets $A_1,\ldots,A_n \subset X$ and any finite subset $F \subset G$ and any $\varepsilon > 0$, there exist Borel subsets $B_1,\ldots,B_n \subset Y$ such that for any $g \in F$ and $i,j \in \{1,\ldots,n\}$, we have
\[
|\mu(g^\alpha(A_i) \cap A_j) - \nu(g^\beta(B_i) \cap B_j)| < \varepsilon.
\]
For two actions $\alpha, \beta \in A(G,X,\mu)$, it is known that $\alpha$ is weakly contained in $\beta$ if and only if $\alpha$ belongs to the weak closure of $[\beta]_\mathit{MC}$ (\ci{Theorem 2.3}{bk}).
For more details on the weak topology on $A(G,X,\mu)$ and weak containment, we refer the reader to \cite{bk} and \cite{ke}.

We say that two actions $\alpha, \beta \in A(G,X,\mu)$ are \textit{orbit equivalent} if there exists $R \in \mathrm{Aut}(X,\mu)$ such that $G^\alpha x = RG^\beta R^{-1} x$ for $\mu$-almost every $x \in X$.
By definition, two measure-conjugate actions in $A(G,X,\mu)$ are orbit equivalent.
For $\alpha \in A(G,X,\mu)$, let $[\alpha]_\mathit{OE}$ denote the set of all actions $\beta \in A(G,X,\mu)$ that are orbit equivalent to $\alpha$.

Lewis Bowen proved the following:

\begin{theorem}[\ci{Theorem 1.1}{bo}]\label{thm-bowen}
Let $G$ be a free group with at most countably many generators.
Then for any $\alpha \in \mathit{FR}(G,X,\mu)$, the set $[\alpha]_\mathit{OE}$ is weakly dense in $A(G, X, \mu)$.
\end{theorem}

Some applications of this result are given in \cite[Remarks 1 and 2]{bo}.
As in \cite[Theorem 1.2]{bo}, it turns out from orbit equivalence rigidity that some non-amenable groups do not satisfy the conclusion of Theorem \ref{thm-bowen}.
In addition to this, any countable group with property (T) does not satisfy the conclusion of Theorem \ref{thm-bowen}.
In fact, if a countable group $G$ has property (T), then the set of all ergodic p.m.p.\ actions of $G$ on $(X,\mu)$ is closed in $A(G,X,\mu)$ and has no interior (see \ci{Theorem 12.2, i)}{ke}, the proof of which is based on \ci{Theorem 1}{gw}).
It follows from the result of \ci{\S 3.1}{ag} mentioned above that all infinite amenable groups satisfy the conclusion of Theorem \ref{thm-bowen}.
Bowen asked the following:

\begin{question}[\ci{Question 1}{bo}]\label{question}
Which countable groups $G$ satisfy the conclusion of Theorem \ref{thm-bowen}?
For example, do all strongly treeable groups (e.g., $\textit{PSL}(2, \mathbb Z)$) satisfy this conclusion?
\end{question}

The goal of this paper is to present a new class of examples of such groups in the following:

\begin{theorem}\label{thm-intro}
Let $G$ be the free product of at most countably many, countably infinite abelian groups.
Then for any $\alpha \in \mathit{FR}(G,X,\mu)$, the set $[\alpha]_\mathit{OE}$ is weakly dense in $A(G,X,\mu)$.
\end{theorem}

Toward the proof of Theorem \ref{thm-intro}, in Section 2, we generalize Bowen's lemma of good partition \ci{Lemma 4.2}{bo}. In Section 3, we prove Theorem \ref{thm-intro}. In contrast with Bowen's proof of Theorem \ref{thm-bowen}, our proof of Theorem \ref{thm-intro} depends on Foreman-Weiss' argument in the proof of \ci{Theorem 16}{fw} and the Rohlin lemma for tiles due to Ornstein-Weiss \ci{II. \S 2, Theorem 5}{ow}. For our purpose, we slightly strengthen the conclusion of the Rohlin lemma for tiles, assuming that the acting group is abelian (Lemma \ref{Rohlin}).
We note that our proof of Theorem \ref{thm-intro} cannot be applied to the case when $G$ is the free product of finite groups, for example, $\textit{PSL}(2,\mathbb Z)$.

\medskip

\textbf{Acknowledgments.}
The author would like to thank his supervisor, Professor Yoshikata Kida, for his helpful comments and enormous support.
The author would also like to thank the anonymous referee for the careful reading of the paper and many helpful suggestions.
This work was supported by the Program for Leading Graduate Schools, MEXT, Japan.

\section{A lemma of good partition}

The aim of this section is to show Lemma \ref{goodpart}, which extends \ci{Lemma 4.2}{bo} to that for the free products of infinite amenable groups.
Let $\alpha \in A(G,X,\mu)$.
For a finite subset $F \subset G$ and a function $f$ on $X$, we define the averaging function $A_{F}^\alpha[f]$ on $X$ by
\[
A_{F}^\alpha[f](x) \coloneqq \frac{1}{|F|} \sum_{g \in F} f(g^{\alpha}x)
\]
for $x\in X$.
Let $\theta \colon (X, \mu)\to (W, \omega)$ be the ergodic decomposition map for the action $\alpha$ with disintegration $\mu =\int_W \mu_w\, d\omega(w)$.
We then set $\mu_x=\mu_{\theta(x)}$ for $x\in X$ and also call the disintegration $\mu =\int_X\mu_x\, d\mu(x)$ the ergodic decomposition of $\mu$ with respect to the action $\alpha$ in the sequel if there is no cause of confusion.

\begin{lemma} \label{goodpart}
Let $G_1,\ldots, G_k$ be countably infinite amenable groups and define $G$ as the free product $G = G_1 \ast \cdots \ast G_k$. Let $\alpha \in \mathit{FR}(G,X,\mu)$ and let $\alpha|G_i$ denote the restriction of $\alpha$ to $G_i$ for each $i\in \{ 1,\ldots,k\}$.
Then for any probability measure $\pi$ on a finite set $\mathcal A$ and any $\varepsilon >0$, there exists a Borel map $\psi \colon X\to \mathcal A$ such that $\psi_\ast \mu = \pi$ and the following holds:
For each $i\in \{ 1,\ldots, k\}$, if $\mu = \int_{X} \mu_x^i \,d\mu(x)$ is the ergodic decomposition of $\mu$ with respect to $\alpha|G_i$, then
\[
\mu(\{\, x \in X \mid \max_{a \in \mathcal A} |(\psi_*\mu_x^i) (a)-\pi(a)| >2\varepsilon \,\}) <\varepsilon.
\]
\end{lemma}

\begin{proof}
The proof basically follows that of \ci{Lemma 4.2}{bo}.
We may assume that $\pi$ is not a measure supported on a single point of $\mathcal{A}$.
Fix $i\in \{ 1,\ldots, k\}$ and pick a F\o lner sequence $\{F_n^i \}_{n\in \mathbb N}$ for $G_i$. Let $s_i$ denote the Bernoulli action $G_i\curvearrowright (\mathcal{A}^{G_i}, \pi^{G_i})$, which is defined by $(g^{s_i}y)(h) =y(hg)$ for $g,h \in G$ and $y \in {\mathcal A}^{G_i}$. We set $C_a^i=\{\, y \in \mathcal A^{G_i} \mid y(e) = a \,\}$ for $a \in \mathcal A$. Then we have
\[
A_{F_n^i}^{s_i}[1_{C_a^i}](y)=\frac{1}{|F_n^i|}\sum_{g\in F_n^i}1_{C_a^i}(g^{s_i}y) = \frac{|\{\, g \in F_n^i \mid y(g) = a \,\}|}{|F_n^i|}
\]
for any $y\in A^{G^i}$. If there is no cause of confusion, we often regard $A_{F_n^i}^{s_i}[1_{C_a^i}]$ as the function on $\mathcal A^{F_n^i}$ defined by the right-hand side of the above equation. According to the $L^1$ version of the mean ergodic theorem (for example, see \ci{Theorem 4.23}{kl}), we have
\[
\lim_{n\to \infty} \| A_{F_n^i}^{s_i}[1_{C_a^i}] - \pi(a) \|_{L^1(\pi^{G_i})} = 0
\]
for every $a \in \mathcal A$. This implies that there exists $n_i \in \mathbb N$ such that if $n\geq n_i$, then
\[
\pi^{G_i} (\{\, y\in \mathcal A^{G_i} \mid \max_{a \in \mathcal A} |A_{F_n^i}^{s_i}[1_{C_a^i}](y) - \pi(a)| >\varepsilon \,\}) < \frac{\varepsilon^2}{2}
\]
and therefore
\begin{equation}\label{pi-fni}
\pi^{F_n^i} (\{\, y\in \mathcal A^{F_n^i} \mid \max_{a \in \mathcal A} |A_{F_n^i}^{s_i}[1_{C_a^i}](y) - \pi(a)| >\varepsilon \,\}) < \frac{\varepsilon^2}{2}.
\end{equation}

We set $n_0=\max_{i\in \{ 1,\ldots,k\}}n_i$.
We set $F^i = F_{n_0}^i$ for the ease of symbols and set $F= \bigcup_{i=1}^{k} F^i$.
We claim that there exists a Borel map $\psi \colon X\to \mathcal A$ such that $\psi_\ast \mu = \pi$ and for each $i\in \{ 1,\ldots,k\}$, if we define a map $\Psi_i \colon  X\to \mathcal A^{F^i}$ by $\Psi_i(x)(g) = \psi(g^{\alpha}x)$ for $x\in X$ and $g \in F^i$, then
\begin{equation}\label{psi_i}
\max_{y \in \mathcal A^{F^i}} |((\Psi_i)_\ast \mu)(y) - \pi^{F^i}(y)|  < \frac{\varepsilon^2}{2M},
\end{equation}
where we set $M = {|\mathcal A|}^{|F|}$.
Indeed, by \ci{Theorem 1}{aw}, the Bernoulli action $G\curvearrowright (\mathcal{A}^G,\pi^G)$, denoted by $s$, is weakly contained in any free p.m.p.\ action of $G$ on $(\mathcal{A}^G,\pi^G)$.
Since both $(X,\mu)$ and $(\mathcal A^G,\pi^G)$ are non-atomic standard probability spaces, there exists a measure-space isomorphism $R \colon (X,\mu) \to (\mathcal A^G,\pi^G)$. Then we see that $s$ belongs to the weak closure of $[R \alpha R^{-1}]_\mathit{MC}$ by \ci{Theorem 2.3}{bk}.
This implies that there exists an automorphism $S \in \mathrm{Aut}(\mathcal A^G, \pi^G)$ such that if $C_a=\{\, y \in \mathcal A^G \mid y(e) = a \,\}$ denotes the cylindrical subset for $a \in \mathcal A$, then
\[
\Biggl| \pi^G \Biggr( \bigcap_{g \in F} SR(g^{-1})^{\alpha}R^{-1}S^{-1} C_{a_g}  \Biggr)  - \pi^G \Biggr( \bigcap_{g \in F} (g^{-1})^s C_{a_g} \Biggr)  \Biggr| < \frac{\varepsilon^2}{2M}
\]
for any $(a_g)_{g \in F} \in \mathcal A^F$. Let $\psi \colon  (X,\mu) \to (\mathcal A, \pi)$ be the measure-preserving map defined by the condition $\psi^{-1}(a)=R^{-1}S^{-1}(C_a)$ for each $a \in \mathcal A$. Then
\[
\Biggl| \mu \Biggr( \bigcap_{g \in F} (g^{-1})^{\alpha} \psi^{-1}(a_g) \Biggr) - \pi^{F} ((a_g)_{g \in F}) \Biggr| < \frac{\varepsilon^2}{2M}
\]
for any $(a_g)_{g \in F} \in \mathcal A^F$, which implies our claim.

We prove that the map $\psi$ is a desired one. Fix  $i \in \{1,\ldots,k\}$. We set
\[Z_i = \{\, x\in X \mid \max_{a\in \mathcal A}|A_{F^i}^{s_i}[1_{C_a}](\Psi_i(x)) - \pi(a)| >\varepsilon \,\}.\]
By inequalities (\ref{pi-fni}) and (\ref{psi_i}), we have
\begin{align*}
\mu(Z_i) &= ((\Psi_i)_\ast \mu)(\{\, y\in \mathcal A^{F^i} \mid \max_{a\in \mathcal A}|A_{F^i}^{s_i}[1_{C_a}](y) - \pi(a)| >\varepsilon \,\}) \\
&< {|\mathcal A|}^{|F^i|}  \max_{y \in \mathcal A^{F^i} } | ((\Psi_i)_\ast \mu)(y) - \pi^{F^i}(y) | + \frac{\varepsilon^2}{2} < \varepsilon^2.
\end{align*}
Let $\mu = \int_{X} \mu_x^i \,d\mu(x)$ be the ergodic decomposition of $\mu$ with respect to the action $\alpha|G_i$.
Then $\int_{X} \mu_x^i(Z_i)\,d\mu(x) = \mu(Z_i) <\varepsilon^2$ and hence
\[
\mu (\{\, x \in X \mid \mu_x^i(Z_i)>\varepsilon \,\}) < \varepsilon.
\]
Suppose that a point $x \in X$ satisfies $\mu_{x}^i(Z_i)\leq \varepsilon$.
Note that for any $a\in \mathcal{A}$ and any $x'\in X$, the following equation holds:
\begin{align*}
A_{F^i}^{s_i}[1_{C_a}](\Psi_i(x'))= \frac{|\{\, g \in F^i \mid \psi(g^\alpha x') = a \,\}|}{|F^i|} =\frac{1}{|F^i|}\sum_{g\in F^i}1_{\psi^{-1}(a)}(g^\alpha x').
\end{align*}
Therefore for any $a\in \mathcal{A}$, we have $\int_X A_{F^i}^{s_i}[1_{C_a}](\Psi_i(x'))\,d\mu_{x}^i(x') = (\psi_\ast \mu_{x}^i)(a)$ and
\begin{align*}
&|(\psi_\ast \mu_{x}^i)(a) - \pi(a) | = \left| \int_X ( A_{F^i}^{s_i}[1_{C_a}](\Psi_i(x')) - \pi(a) ) \, d\mu_{x}^i(x') \right| \\
&\leq \int_{Z_i} | A_{F^i}^{s_i}[1_{C_a}](\Psi_i(x')) - \pi(a) | \, d\mu_{x}^i(x') + \int_{X\setminus Z_i} | A_{F^i}^{s_i}[1_{C_a}](\Psi_i(x')) - \pi(a) | \, d\mu_{x}^i(x') \\
&\leq \mu_{x}^i({Z_i}) + \varepsilon \leq 2\varepsilon.
\end{align*}
Hence
\[
\mu(\{\, x \in X \mid \max_{a \in \mathcal A} |(\psi_*\mu_{x}^i)(a)-\pi(a)| >2\varepsilon \,\}) \leq \mu (\{\, x \in X \mid \mu_{x}^i(Z_i)>\varepsilon \,\}) < \varepsilon.\qedhere
\]
\end{proof}

\section{Proof of the Main Theorem}
A key ingredient of the proof of Theorem \ref{thm-intro} is the Rohlin lemma for tiles.
For a countable group $G$, we say that a finite subset $T$ of $G$ is a {\it tile} for $G$ if there exists a subset $C \subset G$ such that the family $\{Tc\}_{c \in C}$ is pairwise disjoint and $G = \bigcup_{c\in C} Tc$. First let us recall the following fact due to Ornstein-Weiss:

\begin{lemma}[\ci{II.\S 2, Theorem 5}{ow}; see also \ci{Theorem 3.3}{o1}]\label{Rohlintile}
Let $G$ be a countable amenable group and $T$ a tile for $G$. Let $G \curvearrowright (X,\mu)$ be an essentially free p.m.p.\ action.
Then for any $\varepsilon >0$, there exists a Borel subset $B \subset X$ such that the family $\{tB\}_{t\in T}$ is pairwise disjoint and $\mu(\bigcup_{t \in T} tB) > 1-\varepsilon$.
\end{lemma}

Assuming that $G$ is abelian, we strengthen Lemma \ref{Rohlintile} into the following, which will be important in the proof of Theorem \ref{thm-intro}:

\begin{lemma}\label{Rohlin}
Let $G$ be a countable abelian group and $T$ a tile for $G$. Let $G \curvearrowright (X,\mu)$ be an essentially free p.m.p.\ action.
Then for any $\varepsilon >0$ and any Borel subset $A \subset X$ with $\mu(A)<\varepsilon/2$, there exists a Borel subset $B \subset X$ such that the family $\{tB\}_{t\in T}$ is pairwise disjoint, $\mu(\bigcup_{t \in T} tB) > 1-\varepsilon$, and $A \cap B = \emptyset$.
\end{lemma}

\begin{proof}
Since $G$ is amenable and $T$ is a tile, it follows from Lemma \ref{Rohlintile} that there exists a Borel subset $W \subset X$ such that the family $\{tW\}_{t\in T}$ is pairwise disjoint and $\mu(\bigcup_{t\in T} tW) > 1-\varepsilon/2$.
We choose an element $t_0 \in T$ such that $\mu(t_0W \cap A) \leq \mu(tW \cap A)$ for any $t \in T$. Then $\mu(t_0W \cap A) < \varepsilon/(2|T|)$ because otherwise the inequality $\mu(A) \geq \sum_{t \in T} \mu(tW \cap A) \geq \varepsilon/2$ would hold, which contradicts our assumption.

We set $B = (t_0 W) \setminus A$. Then the family $\{tB\}_{t \in T}$ is pairwise disjoint since $G$ is abelian and the family $\{tW\}_{t \in T}$ is pairwise disjoint. Moreover, we have $\mu(B) > \mu(W) - \varepsilon/(2|T|)$ and hence $\mu( \bigcup_{t\in T} tB ) = |T|\mu(B) > |T|\mu(W) - \varepsilon /2 > 1- \varepsilon$.
Therefore the set $B$ is a desired one.
\end{proof}

For finite subsets $F,T \subset G$ and $\varepsilon >0$, we say that $T$ is {\it $(F,\varepsilon)$-invariant} if $|T \bigtriangleup gT| < \varepsilon |T|$ for every $g \in F$.
We say that a countable amenable group $G$ is \textit{monotilable} if there exists a F\o lner sequence $\{ F_n \}_{n \in \mathbb N}$ for $G$ such that each $F_n$ is a tile for $G$. The following fact is briefly mentioned in \ci{I.\S 2, p.22}{ow} and the proof of \ci{Theorem 2}{o2}. We give its proof for the reader's convenience.

\begin{proposition}\label{abtile}
Every countable abelian group is monotilable.
\end{proposition}

\begin{proof}
Let $G$ be a countable abelian group.
If $G$ is finitely generated, then $G$ is isomorphic to the group $\mathbb Z^r \oplus C$ for some non-negative integer $r$ and some finite abelian group $C$. In this case, if we set $F_n = ([-n,n]^r\cap \mathbb Z^r) \oplus C$, then $F_n$ is a tile for $G$ and $\{ F_n \}_{n \in \mathbb N}$ is a F\o lner sequence for $G$, which proves the proposition.
Suppose that $G$ is not finitely generated. Since $G$ is countable, there exists an increasing sequence $\{ G_m \}_{m\in \mathbb N}$ of finitely generated subgroups of $G$ such that $G = \bigcup_{m \in \mathbb N} G_m$. Considering the right coset decomposition of $G$, we see that every tile for $G_m$ is also a tile for $G$. Then for any finite subset $F \subset G$ and any $\varepsilon >0$, choosing $m \in \mathbb N$ such that $F \subset G_m$, we have an $(F,\varepsilon)$-invariant tile $T$ for $G_m$, which is also an $(F, \varepsilon)$-invariant tile for $G$. Thus the proposition follows.
\end{proof}

For the proof of the main result, we also need the following:

\begin{lemma}\label{ergdense}
Let $G_1,\ldots, G_k$ be countably infinite amenable groups and define $G$ as the free product $G = G_1 \ast \cdots \ast G_k$. Then the set of all actions $\alpha \in A(G, X, \mu)$ such that for each $i\in \{ 1, \ldots, k\}$, the restriction $\alpha|G_i$ is essentially free and ergodic is weakly dense in $A(G,X,\mu)$.
\end{lemma}

\begin{proof}
Let $\beta \in A(G,X,\mu)$. Let $F \subset G$ be a finite subset, let $\varepsilon >0$, and let $A_1, \ldots, A_n \subset X$ be Borel subsets.
We choose an $N \in \mathbb N$ and a finite subset $F_i \subset G_i$ for each $i\in \{ 1,\ldots,k\}$ such that $F \subset (F_1 \cup  \cdots \cup F_k)^N$.
We set $L= (F_1 \cup  \cdots \cup F_k)^N$.
Since $G_i$ is amenable, the set of all essentially free ergodic p.m.p.\ actions of $G_i$ is weakly dense in $A(G_i,X,\mu)$ (\ci{Proposition 13.2}{ke}). Hence, for each $i\in \{ 1,\ldots,k\}$, we can choose an essentially free ergodic p.m.p.\ action $\alpha_i$ of $G_i$ on $(X, \mu)$ such that for any $h \in F_i$, $l \in L$ and $j\in \{ 1,\ldots,n\}$, we have
\[
\mu( h^{\alpha_i} (l^{\beta}A_j) \bigtriangleup h^{\beta} (l^{\beta}A_j)) < \frac{\varepsilon}{N}.
\]
Let $\alpha$ be the action of $G$ on $(X, \mu)$ defined by $\alpha|G_i = \alpha_i$ for each $i\in \{ 1,\ldots,k\}$.
Using the inequality
\[
\mu((g_2g_1)^\alpha A \bigtriangleup (g_2g_1)^\beta A) \leq \mu(g_1^\alpha A \bigtriangleup g_1^\beta A) + \mu(g_2^\alpha (g_1^\beta A) \bigtriangleup g_2^\beta (g_1^\beta A))
\]
for $g_1,g_2 \in G$ and a Borel subset $A \subset X$, we have $\mu(g^{\alpha}A_j \bigtriangleup g^{\beta} A_j) < \varepsilon$ for any $g \in F$ and $j\in \{ 1,\ldots,n\}$, which completes the proof of the lemma.
\end{proof}

We now prove our main result for the free product of finitely many, countably infinite abelian groups:

\begin{theorem}\label{main}
Let $G_1,\ldots, G_k$ be countably infinite abelian groups and define $G$ as the free product $G = G_1 \ast \cdots \ast G_k$. Suppose that $\alpha \in \mathit{FR}(G,X,\mu)$ and $\beta \in A(G,X,\mu)$. Let $F \subset G$ be a finite subset, let $\varepsilon >0$, and let $A_1,\ldots,A_n \subset X$ be Borel subsets.
Then there exists $\gamma \in [\alpha]_\mathit{OE}$ such that for any $j\in \{ 1,\ldots,n\}$ and $g\in F$, we have $\mu(g^{\gamma} A_j \bigtriangleup g^\beta A_j) < \varepsilon$.
Therefore for any $\alpha \in \mathit{FR}(G,X,\mu)$, its orbit equivalence class $[\alpha]_{OE}$ is weakly dense in $A(G,X,\mu)$.
\end{theorem}

\begin{proof}
By Lemma \ref{ergdense}, we may assume that for each $i\in \{ 1, \ldots, k\}$, the restriction $\beta|G_i$ is essentially free and ergodic. Moreover, using a similar argument as in the proof of Lemma \ref{ergdense}, we may assume that $F$ is the union $F_1 \cup  \cdots \cup F_k$, where $F_i$ is a finite subset of $G_i$.

We take the finite set $\mathcal A$ and the Borel map $\phi \colon X \to \mathcal A$ such that $\{ \phi^{-1}(a)\}_{a \in \mathcal A}$ is the Borel partition of $X$ generated by the family $\{ g^{\beta}A_j \}_{g\in F, 1\leq j\leq n}$. Let $\varepsilon' = \varepsilon/(24|\mathcal A|)$. By applying Lemma \ref{goodpart} to the action $\alpha$, the probability measure $\phi_\ast \mu$ on $\mathcal A$, and the number $\varepsilon'$, we obtain a Borel map $\psi \colon X\to \mathcal A$ such that $\psi_\ast \mu = \phi_\ast \mu$ and for each $i\in \{ 1,\ldots,k\}$, if $\mu = \int_{X} \mu_x^i \,d\mu(x)$ is the ergodic decomposition of $\mu$ with respect to $\alpha|G_i$, we have
\[
\mu(\{\, x\in X \mid \max_{a \in \mathcal A} |(\psi_\ast\mu_x^i)(a)-(\psi_\ast\mu)(a) | >2\varepsilon' \,\}) <\varepsilon'.
\]
Since $\psi_\ast \mu = \phi_\ast \mu$ and $(X,\mu)$ is a non-atomic standard probability space, there exists $R \in \mathrm{Aut}(X,\mu)$ such that $R(\psi^{-1}(a)) = \phi^{-1}(a)$ for all $a\in \mathcal A$. We set $\alpha' = R\alpha R^{-1} \in \mathit{FR}(G,X,\mu)$ and set $\alpha_i = \alpha|G_i$, $\alpha'_i = \alpha'|G_i$ and $\beta_i = \beta|G_i$.
We fix $i \in \{1,\ldots,k\}$ throughout Claims \ref{erg+Rohlin}-- \ref{weakapp}.

\begin{claim}\label{erg+Rohlin}
There exist Borel subsets $B^{\alpha'_i}, B^{\beta_i} \subset X$ and an $(F_i,\varepsilon')$-invariant tile $T$ for $G_i$ such that $\mu(B^{\alpha'_i})=\mu(B^{\beta_i})$, $e \in T$, $|T| > 1/\varepsilon'$, and the following conditions (1)--(3) and (1')--(3') hold:

\begin{enumerate}
\item The family $\{ t^{\alpha'_i} B^{\alpha'_i} \}_{t\in T}$ is pairwise disjoint.
\item We have $\mu ( \bigcup_{t\in T} t^{\alpha'_i}B^{\alpha'_i} ) > 1-8\varepsilon'$.
\item For all $x \in B^{\alpha'_i}$ and $a \in \mathcal A$, we have
\[
\left| \displaystyle\frac{ |\{\, t\in T \mid t^{\alpha'_i}x \in \phi^{-1}(a) \,\}| }{|T|} - \mu(\phi^{-1}(a)) \right| \leq 3\varepsilon'.
\]
\end{enumerate}
\begin{enumerate}
\renewcommand{\labelenumi}{(\arabic{enumi}')}
\item The family $\{ t^{\beta_i} B^{\beta_i} \}_{t\in T}$ is pairwise disjoint.
\item We have $\mu ( \bigcup_{t\in T} t^{\beta_i}B^{\beta_i} ) > 1-8\varepsilon'$.
\item For all $x \in B^{\beta_i}$ and $a \in \mathcal A$, we have
\[
\left| \displaystyle\frac{ |\{\, t\in T \mid t^{\beta_i}x \in \phi^{-1}(a) \,\}| }{|T|} - \mu(\phi^{-1}(a)) \right| \leq 3\varepsilon'.
\]
\end{enumerate}
\end{claim}

\begin{proof}
By the proof of Proposition \ref{abtile}, there exists a F\o lner sequence $\{D_n\}_{n\in \mathbb N}$ for $G_i$ such that each $D_n$ is a tile for $G_i$ and contains the identity $e$.
Note that for any $\delta \in A(G_i, X, \mu)$ and any Borel subset $C\subset X$, we have
\[
A_{D_n}^\delta[1_{C}](x) = \displaystyle\frac{ |\{\, g\in D_n \mid g^{\delta}x \in C \,\}| }{|D_n|}
\]
for any $x\in X$.
By the $L^1$ version of the mean ergodic theorem, it follows that for each $a\in \mathcal A$, we have
\[
\displaystyle\lim_{n\to \infty} \| A_{D_n}^{\alpha_i}[1_{\psi^{-1}(a)}] - \mathbb E(1_{\psi^{-1}(a)}) \|_{L^1(\mu)} = 0,
\]
where $\mathbb E(1_{\psi^{-1}(a)})$ is the conditional expectation of $1_{\psi^{-1}(a)}$ onto the space of $\alpha_i$-invariant functions in $L^1(X,\mu)$. Then there exists $n_1 \in \mathbb N$ such that for every $n \geq n_1$, we have
\[
 \mu(\{\, x\in X \mid \ \max_{a\in \mathcal A}| A_{D_n}^{\alpha_i}[1_{\psi^{-1}(a)}](x) - \mathbb{E}(1_{\psi^{-1}(a)})(x) | > \varepsilon' \,\} ) < \varepsilon'.
\]
Recall that $\mu =\int_X\mu_x^i\, d\mu(x)$ denotes the ergodic decomposition of $\mu$ with respect to $\alpha_i$. Then $\mathbb{E}(1_{\psi^{-1}(a)})(x) = \mu_x^i(\psi^{-1}(a))$ for any $a\in \mathcal{A}$ and $\mu$-almost every $x \in X$. We set
\[
X_n^{\alpha_i} = \{\, x\in X \mid \ \max_{a \in \mathcal A}| A_{D_n}^{\alpha_i}[1_{\psi^{-1}(a)}](x) - \mu_x^i(\psi^{-1}(a)) | \leq \varepsilon' \  \text{and} \ \max_{a\in \mathcal A} |(\psi_\ast \mu_x^i)(a)-(\psi_\ast\mu)(a)|  \leq 2\varepsilon'  \,\}
\]
for $n \in \mathbb N$. Then $\mu(X_n^{\alpha_i}) > 1-2\varepsilon'$ for every $n \geq n_1$.
If $x \in X_n^{\alpha_i}$, then for each $a \in \mathcal A$, we have
\begin{align*}
& \left| A_{D_n}^{\alpha_i}[1_{\psi^{-1}(a)}](x) - \mu(\psi^{-1}(a)) \right| \\
&\leq \left| A_{D_n}^{\alpha_i}[1_{\psi^{-1}(a)}](x) - \mu_x^i (\psi^{-1}(a)) \right| + |\mu_x^i (\psi^{-1}(a)) - \mu(\psi^{-1}(a))| \leq \varepsilon' + 2\varepsilon' = 3\varepsilon'.
\end{align*}
We set $X_n^{\alpha'_i} = RX_n^{\alpha_i}$. For each $g \in G_i$ and $x\in X$, by the definition of $R$ and $\alpha'$, we have $g^{\alpha_i}x \in \psi^{-1}(a)$ if and only if $g^{\alpha'_i}Rx \in \phi^{-1}(a)$. Combining this with $\psi_\ast \mu = \phi_\ast \mu$, for all $x\in X_n^{\alpha'_i}$ and $a\in \mathcal A$, we have
\[
\left| A_{D_n}^{\alpha'_i}[1_{\phi^{-1}(a)}](x) - \mu(\phi^{-1}(a)) \right| \leq  3\varepsilon'.
\]
On the other hand, since $\beta_i$ is ergodic, there is $n_2 \in \mathbb N$ such that for every $n \geq n_2$, we have
\[
\mu( \{\, x \in X \mid | A_{D_n}^{\beta_i} [1_{\phi^{-1}(a)}](x) - \mu(\phi^{-1}(a)) | > 3\varepsilon' \,\} ) < 2\varepsilon'.
\]
We set $X_n^{\beta_i} = \{\, x \in X \mid \max_{a\in \mathcal{A}}| A_{D_n}^{\beta_i} [1_{\phi^{-1}(a)}](x) - \mu(\phi^{-1}(a)) | \leq 3\varepsilon' \,\}$.

We construct Rohlin towers for $\alpha_i'$ and $\beta_i$. Let $m$ be an integer such that $m \geq \max\{n_1,n_2\}$ and $|D_{m}| > 1/\varepsilon'$. We set $A=X \setminus (X_{m}^{\alpha'_i} \cap X_{m}^{\beta_i})$ and set $T=D_{m}$. Since $\mu(X_{m}^{\alpha'_i}) > 1-2\varepsilon'$ and $\mu(X_{m}^{\beta_i}) > 1-2\varepsilon'$, we have $\mu(A) < 4\varepsilon'$. We apply Lemma \ref{Rohlin} to the tile $T$ and the Borel subset $A \subset X$, and then obtain Borel subsets $B^{\alpha_i'}, B^{\beta_i} \subset X$ disjoint from $A$ and satisfying conditions (1), (2), (1') and (2'). Since $B^{\alpha_i'}$ and $B^{\beta_i}$ are disjoint from $A$, conditions (3) and (3') also hold. After replacing one of $B^{\alpha'_i}$ and $B^{\beta_i}$ into its Borel subsets, we may further assume that $\mu(B^{\alpha'_i}) = \mu(B^{\beta_i})$.
\end{proof}

\begin{claim}\label{basepart}
Let $B^{\alpha'_i}, B^{\beta_i}\subset X$ be the Borel subsets and $T$ the tile for $G$ chosen in Claim \ref{erg+Rohlin}.
Then there exist finite Borel partitions $\{ Q_s^{\alpha'_i} \}_{s=1}^r$ and $\{ Q_s^{\beta_i} \}_{s=1}^r$ of $B^{\alpha'_i}$ and $B^{\beta_i}$, respectively, such that for each $s \in \{ 1,\ldots,r\}$, the following properties hold:
\begin{enumerate}
\renewcommand{\labelenumi}{(\alph{enumi})}
\item The equation $\mu(Q_s^{\alpha'_i}) = \mu(Q_s^{\beta_i})$ holds.
\item For every $t\in T$, we have $t^{\alpha'_i} Q_s^{\alpha'_i} \subset \phi^{-1}(a)$ and $t^{\beta_i} Q_s^{\beta_i} \subset \phi^{-1}(a')$ for some $a,a' \in \mathcal A$.
\item There exist a subset $T_s\subset T$ and a permutation $\sigma_s$ of $T$ such that $|T \setminus T_s| < 7 \varepsilon' |\mathcal A||T|$, $\sigma_s(e)=e$, and for any $t \in T_s$ and any $a \in \mathcal A$, we have
\begin{equation}\label{equiv1}
\sigma_s(t)^{\alpha'_i}Q_s^{\alpha'_i} \subset \phi^{-1}(a) \Leftrightarrow t^{\beta_i} Q_s^{\beta_i} \subset \phi^{-1}(a).
\end{equation}
\end{enumerate}
\end{claim}

\begin{proof}
We rely on the proof of \cite[Theorem 16]{fw}.
Let $\{ P_l^{\alpha'_i}\}_l$ be the finite partition of $B^{\alpha'_i}$ generated by $\{ (t^{-1})^{\alpha'_i}(t^{\alpha'_i}B^{\alpha'_i} \cap \phi^{-1}(a))  \}_{t\in T, a \in \mathcal A}$, and $\{ P_m^{\beta_i}\}_m$ be the finite partition of $B^{\beta_i}$ generated by $\{ (t^{-1})^{\beta_i}(t^{\beta_i}B^{\beta_i} \cap \phi^{-1}(a))  \}_{t\in T, a \in \mathcal A}$. Since $\mu(B^{\alpha_i'})=\mu(B^{\beta_i})$, we can take a refinement $\{ Q_s^{\alpha'_i} \}_{s=1}^r$ of $\{ P_l^{\alpha'_i}\}_l$ and a refinement $\{ Q_s^{\beta_i} \}_{s=1}^r$ of $\{ P_m^{\beta_i} \}_m$ such that $\{ Q_s^{\alpha'_i} \}_{s=1}^r$ and $\{ Q_s^{\beta_i} \}_{s=1}^r$ satisfy condition (a). By the construction of $\{ P_l^{\alpha'_i}\}_l$ and $\{ P_m^{\beta_i}\}_m$, they also satisfy condition (b).

We fix $s \in \{1,\ldots,r \}$. We find a subset $T_s$ of $T$ and a permutation $\sigma_s$ of $T$ which satisfy condition (c). By conditions (3) and (3') in Claim \ref{erg+Rohlin}, we have
\[
\left| |\{\, t\in T \mid t^{\alpha'_i}x \in \phi^{-1}(a) \,\} | - | \{\, t\in T \mid t^{\beta_i}x' \in \phi^{-1}(a) \,\} | \right| \leq 6\varepsilon'|T|,
\]
for any $a \in \mathcal A$, $x \in B^{\alpha'_i}$ and $x' \in B^{\beta_i}$.
For each $a\in \mathcal A$, the set $\{\, t\in T \mid t^{\alpha'_i}x \in \phi^{-1}(a) \,\}$ is independent of $x\in Q_s^{\alpha'_i}$ because of part (b) of the claim, which has been established already. The same is true for $\beta_i$ in place of $\alpha_i'$.
Therefore we can choose a bijection $\sigma_s \colon T \to T$ such that $\sigma_s(e)=e$ and for each $a\in \mathcal A$, we have
\[
| \sigma_s( \{\, t\in T \mid t^{\beta_i}Q_s^{\beta_i} \subset \phi^{-1}(a) \,\} ) \setminus \{\, t\in T  \mid t^{\alpha'_i}Q_s^{\alpha'_i} \subset \phi^{-1}(a) \,\} | \leq 6\varepsilon'|T|+1.
\]
The condition $\sigma_s(e)=e$ will be used in the proof of Claim \ref{weakapp}. We set
\[
T_s = \{\, t \in T \mid t^{\beta_i}Q_s^{\beta_i}\subset \phi^{-1}(a)\ \text{and}\ \sigma_s(t)^{\alpha'_i}Q_s^{\alpha'_i}\subset \phi^{-1}(a)\ {\rm for\ some\ }a\in \mathcal A \,\}.
\]
Then $|T \setminus T_s| \leq (6 \varepsilon' |T|+1)|\mathcal A| < 7\varepsilon'|\mathcal A||T|$ since $|T| > 1/\varepsilon'$, and condition (\ref{equiv1}) holds for any $t \in T_s$ and any $a\in \mathcal A$.
\end{proof}

For an action $\delta \in A(G,X,\mu)$, let $[\delta]_\mathit{SO}$ denote the set of all actions $\eta \in A(G,X,\mu)$ that have the same orbits as $\delta$, i.e., satisfy $G^\delta x = G^\eta x$ for $\mu$-almost every $x \in X$.

\begin{claim}\label{weakapp}
There exists $S_i \in \mathrm{Aut}(X,\mu)$ such that the action $\alpha''_i \coloneqq S_i \alpha'_i S_i^{-1}$ belongs to $[\alpha'_i]_\mathit{SO}$ and for any $g \in F_i$ and any $j\in \{ 1,\ldots,n\}$, we have $\mu(g^{\alpha''_i} A_j \bigtriangleup g^{\beta_i} A_j) < \varepsilon$.
\end{claim}

\begin{proof}

We define $S_i \in \mathrm{Aut}(X,\mu)$ by $S_i = \sigma_s(t)^{\alpha'_i}(t^{-1})^{\alpha'_i}$ on $t^{\alpha'_i}Q_s^{\alpha'_i}$ for $s\in \{ 1,\ldots,r\}$ and $t \in T$ and by $S_i = \text{id}$ on $X \setminus TB^{\alpha'_i}$. We set $\alpha''_i=S_i \alpha'_i S^{-1}_i$. Then $\alpha''_i \in [\alpha'_i]_\mathit{SO}$, and $S_iQ_s^{\alpha_i'}=Q_s^{\alpha_i'}$ since $e\in T$ and $\sigma_s(e)=e$.
By condition (\ref{equiv1}), for any $s\in \{ 1,\ldots,r\}$, any $t \in T_s$ and any $a\in \mathcal A$, we have
\begin{equation}\label{equiv2}
t^{\alpha''_i}Q_s^{\alpha'_i} \subset \phi^{-1}(a) \Leftrightarrow t^{\beta_i} Q_s^{\beta_i} \subset \phi^{-1}(a)
\end{equation}
since $S_i t^{\alpha'_i} S^{-1}_i Q_s^{\alpha'_i} = \sigma_s(t)^{\alpha'_i} Q_s^{\alpha'_i}$.

Fix $g \in F_i$ and $j \in \{1,\ldots,n\}$ arbitrarily.
We set
\[L_0 = X \setminus \bigcup_{t\in T} t^{\alpha''_i}B^{\alpha'_i},\quad L_1 = \bigcup_{t\in T \setminus gT} t^{\alpha''_i}B^{\alpha'_i}\quad \text{and} \quad L_2 = \bigcup_{s=1}^{r}\bigcup_{t \in T \setminus (T_s \cap gT_s)} t^{\alpha''_i}Q_s^{\alpha'_i},\]
We estimate the measures of $L_0$, $L_1$ and $L_2$. We have $\mu(L_0) < 8\varepsilon'$ by condition (2) in Claim \ref{erg+Rohlin}.
Since the set $T$ is $(F_i,\varepsilon')$-invariant and $g \in F_i$, we have $|T \setminus gT| < \varepsilon' |T|$ and hence $\mu(L_1) < \varepsilon'|T|\mu(B^{\alpha'_i}) \leq \varepsilon'$.
Since $|T \setminus gT_s| \leq |T \setminus gT| + |gT \setminus gT_s| = |T \setminus gT| + |T \setminus T_s|$, we have
\[
\mu(L_2) \leq \sum_{s=1}^{r}(|T \setminus gT| + 2|T \setminus T_s|)\mu(Q_s^{\alpha'_i}) < (\varepsilon'|T| + 14\varepsilon'|\mathcal A||T|)\mu(B^{\alpha'_i}) \leq 15|\mathcal A|\varepsilon'.
\]

We claim that $\mu ( (g^{\alpha''_i} A_j \bigtriangleup g^{\beta_i} A_j) \setminus ( L_0 \cup L_1 \cup L_2 ) ) = 0$.
Suppose otherwise, i.e., some $s \in \{1,\ldots,r\}$ and $t \in gT \cap (T_s \cap gT_s)$ satisfy $\mu(t^{\alpha''_i}Q_s^{\alpha'_i} \cap (g^{\alpha''_i} A_j \bigtriangleup g^{\beta_i} A_j)) >0$. By condition (\ref{equiv2}), there exists $a \in \mathcal A$ such that
\begin{equation}\label{cond1}
t^{\alpha''_i}Q_s^{\alpha'_i} \subset \phi^{-1}(a) \quad \text{and} \quad t^{\beta_i}Q_s^{\beta_i} \subset \phi^{-1}(a),
\end{equation}
and there exists $a'\in \mathcal{A}$ such that
\begin{equation}\label{cond2}
{(g^{-1}t)}^{\alpha''_i}Q_s^{\alpha'_i} \subset \phi^{-1}(a') \quad \text{and} \quad {(g^{-1}t)}^{\beta_i}Q_s^{\beta_i} \subset \phi^{-1}(a').
\end{equation}
If $\mu(t^{\alpha''_i}Q_s^{\alpha'_i} \cap (g^{\alpha''_i} A_j \setminus g^{\beta_i} A_j)) >0$, then by condition (\ref{cond2}), we have $\phi^{-1}(a') \subset A_j$ and hence $t^{\beta_i} Q_s^{\beta_i} \subset g^{\beta_i} A_j$. Combining this with condition (\ref{cond1}), we have $\phi^{-1}(a) \subset g^{\beta_i}A_j$ and hence $t^{\alpha''_i}Q_s^{\alpha'_i} \subset g^{\beta_i}A_j$, which contradicts the assumption $\mu(t^{\alpha''_i}Q_s^{\alpha'_i} \cap (g^{\alpha''_i} A_j \setminus g^{\beta_i} A_j)) >0$.
On the other hand, if $\mu(t^{\alpha''_i}Q_s^{\alpha'_i} \cap (g^{\beta_i} A_j \setminus g^{\alpha''_i} A_j)) >0$, then by condition (\ref{cond1}), we have $\phi^{-1}(a) \subset g^{\beta_i}A_j$ and hence $(g^{-1}t)^{\beta_i}Q_s^{\beta_i} \subset A_j$. Combining this with condition (\ref{cond2}), we have $\phi^{-1}(a') \subset A_j$ and hence $t^{\alpha''_i}Q_s^{\alpha'_i} \subset g^{\alpha''_i}A_j$, which contradicts the assumption $\mu(t^{\alpha''_i}Q_s^{\alpha'_i} \cap (g^{\beta_i} A_j \setminus g^{\alpha''_i} A_j)) >0$.
Therefore we have  $\mu(t^{\alpha''_i}Q_s^{\alpha'_i} \cap (g^{\alpha''_i} A_j \bigtriangleup g^{\beta_i} A_j)) =0$ for any $s \in \{ 1,\ldots,r\}$ and any $t \in gT \cap (T_s \cap gT_s)$. As a result, we have $\mu ( (g^{\alpha''_i} A_j \bigtriangleup g^{\beta_i} A_j) \setminus ( L_0 \cup L_1 \cup L_2 ) ) = 0$ and
\[
\mu ( g^{\alpha''_i} A_j \bigtriangleup g^{\beta_i} A_j) \leq \mu(L_0) + \mu(L_1) + \mu(L_2) < 8\varepsilon' + \varepsilon' + 15|\mathcal A|\varepsilon' \leq 24|\mathcal A|\varepsilon' =\varepsilon.
\]
This holds for any $g \in F_i$ and any $j\in \{ 1,\ldots,n\}$.
\end{proof}

Let $\gamma \in A(G, X, \mu)$ be the action defined by $\gamma |G_i = \alpha''_i$ for each $i\in \{ 1, \ldots, k\}$. Then we have $\gamma \in [\alpha]_\mathit{OE}$ since $\alpha' \in [\alpha]_\mathit{MC}$ and $\alpha''_i \in [\alpha'_i]_\mathit{SO}$ for every $i\in \{ 1,\ldots,k\}$.
Claim \ref{weakapp} shows that $\gamma$ is the desired action.
This completes the proof of Theorem \ref{main}.
\end{proof}

\begin{proof}[Proof of Theorem \ref{thm-intro}]
It remains to show the theorem for a free product of (countably) infinitely many, infinite abelian groups. We show this, following \ci{Corollary 2.2}{bo}.
Let $G=G_1 \ast G_2 \ast \cdots$ be the free product of infinite abelian groups $G_i$ with $i\in \mathbb N$.
Suppose that $\alpha \in \mathit{FR}(G,X,\mu)$ and $\beta \in A(G,X,\mu)$. Let $F \subset G$ be a finite subset, let $\varepsilon >0$, and let $A_1,\ldots,A_n \subset X$ be Borel subsets. We set $H_k = G_1 \ast \cdots \ast G_k$ for $k \in \mathbb N$. Pick $k \in \mathbb N$ such that $F \subset H_k$. By Theorem \ref{main}, there exists an action $\alpha' \in A(H_k,X,\mu)$ such that $\alpha' \in [\alpha|H_k]_\mathit{OE}$ and $\mu(g^{\alpha'} A_j \bigtriangleup g^{\beta} A_j ) < \varepsilon$ for any $g \in F$ and $j\in \{ 1,\ldots,n\}$. Since $\alpha' \in [\alpha|H_k]_\mathit{OE}$, there exists $R \in \mathrm{Aut}(X,\mu)$ such that $R^{-1} \alpha' R \in [\alpha|H_k]_\mathit{SO}$. We define an action $\gamma \in A(G,X,\mu)$ by $\gamma|H_k = \alpha'$ and $g^{\gamma} = Rg^{\alpha}R^{-1}$ for $g \in G_m$ with $m \geq k+1$. Then $\gamma$ is orbit equivalent to $\alpha$ via $R$ and satisfies $\mu(g^\gamma A_j\bigtriangleup g^\beta A_j)<\varepsilon$ for any $g\in F$ and $j\in \{ 1,\ldots, n\}$.
\end{proof}

redpajama_set_name: RedPajamaArXiv


いざ!秋の美瑛へ!ちょっとその前に。Awfully! To Biei in autumn! Before that.
絶景かなIt is a magnificent view.
The world is in the midst of Christmas. How are you doing?
I was planning to raise Christmas-like photographs like Hokkaido of illumination and snow, but since there was not much good, I decided to raise the picture of Biei so far.
This is also the famous shooting spot of "Biei" Christmas tree tree ".
If it was originally blue sky or snowy landscape it would have been very nice, but unfortunately it was rainy on this day.Travel photos can not be controlled until the weather. But I think that is good. There are also good pictures of rain.
Well this time it is Christmas!
Manual mode : F6.3 SS:1/250s ISO:100 WB=Manual.
Manual mode : F4.5 SS:1/200s ISO:100 WB=Manual.


text:
Roberta HERRERA
Cartier develops its program dedicated to female entrepreneurship
Empowering female entrepreneurs to drive change is the ultimate goal of the Cartier Women's Initiative. The project launched in 2006 by the luxury jewelry firm aims to build an international community of female entrepreneurs, reward innovative ideas, and provide financial, social, and human capital support to businesses that create a positive social and environmental impact. With a 15-year track record under its belt, the program is gearing up for the next awards event in 2023 with the aim of continuing to grow and foster partnerships.
The initiative of the luxury brand owned by the Richemont group already has 262 members from 62 countries and has awarded a total of 6 million euros to previous winners. The registration period for future participants from any country or industry opened on May 16 and will close on June 30 on the company's website.
Cyrille Vigneron, Cartier International CEO - Cartier
"Women entrepreneurs drive economic growth and social and environmental impact but are still facing staggering barriers. Via the Cartier Women's Initiative, we hope to drive change by empowering women impact entrepreneurs, by providing financial, social and human capital support," said Wingee Sampaio, global program director of the initiative. In 2023, the seven existing regional categories will be joined by French-speaking Sub-Saharan Africa and Oceania.
This edition will also feature the annual Impact Awards honoring businesses that preserve the planet, improve living conditions in underprivileged communities and create opportunities, as well as a Science and Technology Pioneer Award and another newly created award dedicated to diversity, equity and inclusion. While the other awards are exclusively limited to female applicants, the latter will be open to all genders.
A "safe space" for women
The projects awarded by the platform extend far beyond the luxury, fashion and jewelry sectors, with a diverse selection of categories ranging from artificial intelligence to educating communities. They all, however, share a pioneering spirit, a willingness to improve society, and face difficulties in developing their business in a corporate world dominated by economic profitability and men in key decision-making positions. The participants respond to these challenges with results driven by a sense of solidarity.
"In addition to increasing our visibility and gaining knowledge, contacts and funding, we feel we are in a safe space where we can share our insecurities and doubts in a women's initiative," explained Nneka Mobisson, founder of mDoc, a chronic disease treatment enterprise in Africa.
Wingee Sampaio, Cartier's Women Initiative - Cartier
"You have to learn how to communicate with investors which is not an easy feat," said Pakistani entrepreneur Mariel Salahuddin, who left a senior position in an energy company to launch a barter-based business that facilitates access to essential goods in rural communities. "The program has opened doors for us in terms of support, mentoring and funding to help scale our business," she said, "We are no longer considered a risky investment."
"Being a female entrepreneur can be very isolating. Being part of this community allows us to share our ideas with women from all over the world, creating a network where projects come to life," explained Australian businesswoman Joanne Howarth, founder of the recycling company Planet Protector Packaging. This sentiment was shared by Temie Giwa-Tubosun, founder of the African medical data and distribution company Life Bank.
"I've never been to an event with so many women; I wish they were all like this. It makes you feel at ease and fuels you with energy. This platform is an opportunity to meet women who share the same problems: from how to raise funds to the best way to approach business meetings," said the entrepreneur, who was awarded during the last awards ceremony, which took place in March at the Dubai Opera House.
Rasha Rady, founder of the Egyptian medical monitoring platform Chefaa, was also optimistic. "There is a huge amount of change happening. Women are now also sitting around the table talking business," she said, underlining the positive impact and guaranteed credibility of having a company like Cartier's support.
A commitment to gender equality at the Dubai Expo 2020
"If we want to find solutions to the many issues at hand, the most logical thing to do is to give women a voice. Gender issues start at home. We leaders and CEOs must set an example. It is our responsibility to correct poor behavior," said Cyrille Vigneron, chairman and CEO of Cartier, during a feminist speech delivered at an evening event on March 8, coinciding with International Women's Day.
Women's Pavilion - Cartier
The latest Cartier Women's Initiative ceremony took place under the impressive Al Wasln dome located at the heart of Dubai Expo 2020, held two years late due to the pandemic. Cartier not only celebrated the 15th anniversary of its awards, but also highlighted its commitment to gender equality by calling for collective action amidst a challenging landscape.
In front of a group of UAE representatives and hundreds of local and foreign guests, Cartier's CEO for the Middle East, India and Africa, Sophie Doireau, took the floor to condemn the war in Ukraine. "Equality, democracy and peace are an obligation for all generations," she said.
The president of the European Commission, Ursula Gertrud von der Leyen, also addressed the crowd that same evening via a recorded video message. "We need all the talent in the world as well as fresh and innovative ideas to regenerate our economy. We cannot afford to leave women out. The time to act is now and we all carry responsibility. The cost of failing to react will be very high," she said at the gala where Cartier ambassador Rami Malek also made a speech defending women's rights.
"When women thrive, humanity thrives," said Reem Al Hashimy, UAE minister of state for international cooperation and CEO of Dubai Expo 2020, which hosted the first Women's Pavilion at a world expo after 3.5 years in the making. The space sponsored by Cartier featured insights and stories about remarkable women and explored concrete challenges and strategies towards achieving gender equality. An immersive art space was also developed in collaboration with French actress and filmmaker Melanie Laurent. Throughout the six-month-long event, the pavilion hosted 150 presentations by female ministers of equality from around the world and offered a learning program for children.
During that same day, Cartier, founded in 1847, held a series of seminars entitled "Break the Bias" in the exhibition's conference center. Participants were able to attend inspirational discussions joined by prominent figures from various different fields such as Sheikha Lubna Al Qasimi, former UAE minister of state for tolerance; Sheryl Sandberg, COO of Facebook; Dr. Natalia Kanem, executive director of UNFPA; and actors Yara Shahidi, Hend Sabry and Edgar Ramirez.
"We have already considered our next steps in our ongoing efforts, which include strengthening cooperation and coalitions that bring together the public and private sectors," explained Vigneron regarding the continuation of the project and the Richemont group's next action plan for fighting gender inequality.
In the last fiscal year, Richemont ranked as the second largest luxury conglomerate in the world. The owner of companies such as Chloé, Montblanc and Yoox Net-a-porter recorded sales of €13.1 billion, down 8% from the €14.2 billion posted in 2020. The jewelry division, which includes brands Buccellati, Cartier and Van Cleef & Arpels, accounted for 57% of total revenues, with sales of €7.5 billion, an increase from €7.2 billion a year earlier.
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text:
Before the shooting, Gilroy and its garlic festival created powerful memories of their own
Josh Susong
The Republic | azcentral.com
PHOENIX – For a little spot on the map deep in farm country, Gilroy holds an outsize place in the minds of millions in Northern California.
The city is a waypoint on the route to nearly everywhere else in the state. It's the heart of a region with scenery that has been immortalized by creators from Steinbeck to Hitchcock.
And always, Gilroy has been inseparable from the identity, flavor and scent of its signature crop: garlic. That crop gave rise to a garlic festival that has, for more than 40 years, celebrated the pungent root in all its permutations.
The Gilroy Garlic Festival features all the same carnival fare of any small-town summertime festival. But the highlight is not the midway, it's the sweltering epicurean mash-up known as Gourmet Alley.
The fare is fiery: Garlic fries, garlic calamari, even garlic ice cream. The flavors linger. A new deal promoted on the carnival's website for 2019: A half-loaf of garlic bread when you exit through gates 3 or 5. ("Take home some delicious garlicky goodness to go!")
The festival is hard not to love. Its universal odor quickly strips away any semblance of self-consciousness and replaces it with good humor.
That good humor was pierced in an instant Sunday night, the last day of the event, when one or more gunmen opened fire into a crowd. Initial reports were confused, but perhaps three people were killed along with a suspect, and a dozen more were wounded, as police continued to swarm the scene.
Northern California shooting:'Incredibly disheartening': 3 killed, 15 wounded in Gilroy Garlic Festival shooting
San Jose resident Angela Escarcega was in line to get garlic bread when the shots began. She fled with her 9-year-old son in her arms.
Natalie Martinez, a Gilroy resident, told the San Jose Mercury News that she had walked to the food stands, separated from her two daughters, when the shooting started. "I thought, we're open prey," she said. "It was awful."
In that moment, Gilroy and its garlic festival joined an American list. One by one, mass shootings have seared into national memory the names of towns that otherwise would have been left to their local identities: San Bernardino. Orlando. Las Vegas. Columbine. Sandy Hook. Parkland.
A signature crop, an annual festival
Gilroy, before Sunday, held a place not in the national identity but at the pinnacle of a regional one.
In the agricultural bounty of California's coastal valleys, towns bear forth their signature crops, with a picking season and festival to match.
Watsonville has its strawberries, their lined fields glinting back the sunlight across Monterey Bay. Castroville has its artichokes. Farther south, the foggy cool of the Salinas Valley spills over with leafy greens from the "Salad Bowl of the World."
But for a signature crop, perhaps no place tops Gilroy.
When the breeze is right, you can smell Gilroy from miles away. The odorous bulb is so central to Gilroy's identity, its shape forms the curlicue tail of the lowercase "g" in the city's logo. It is, proudly, the Garlic Capital of the World.
The festival dates to 1979, when a local college president persuaded the region's biggest farmers to pitch in and celebrate the crop. Back then, as the festival's website tells it, the aroma of garlic was something not often shared in polite company, and some in Gilroy were "more embarrassed about Gilroy's garlic heritage (and the town's distinctive odor) than proud of it."
That changed quickly, as the festival grew, raising millions over the years for local charities, and drawing more than 100,000 people each year to a festival in the height of summer.
A city on the road to everywhere
For millions in the Bay Area, Gilroy in any season is the only real way to reach Interstate 5 and its beeline toward Los Angeles. You traverse Gilroy's pungent fields on a narrow road still shared with farm trucks, then climb Pacheco Pass, where the last breath of coastal California is the highway stop called Casa de Fruta.
What we know:3 dead, 15 wounded: What we know about the Gilroy Garlic Festival shooting
Gilroy is also the last breath of the Bay Area's counties when headed for the scenic Central Coast. Any Hitchcock fan in the car will recognize the road. It was here that James Stewart and Kim Novak raced toward the fateful bell tower scene at San Juan Bautista.
Beyond Gilroy lie the Gabilan Mountains, so beautiful that John Steinbeck's character in "The Red Pony" named his beloved pony after the range.
But Gilroy's festival is set in the foothills of the Santa Cruz range, where the remains of the Bay Area's redwoods give way to the last of its farm fields. The city's Christmas Hill Park has hosted the festival since its second year.
These days, the festival is so crowded that most park far away and ride a shuttle bus in. Tour bus operators stage their buses at Gavilan College, three miles south of the park.
On Sunday night, the college campus instead became the site for families looking for loved ones who survived the chaos.
"If you are looking for a loved one, please go to the reunification center at Gavilan College," Gilroy police posted on Twitter. "As a reminder please do not come to Christmas Hill Park, this is still an active crime scene."
Tragedy overshadows tradition
By Sunday night, news groups were arriving at Gilroy. Police units from as far away as San Jose to the north and Monterey County to the south. The ATF. The FBI.
And Gilroy and its garlic festival, until now famous only in the flavors of Northern California, became famous for the worst of reasons.
Shortly after 10 p.m. PDT, as Gilroy Police Chief Scot Smithee approached the microphones for a news conference, he seemed to recognize both the incredible circumstances and tragic familiarity of the scene.
"This is one of those press conferences you never want to have to give," he said.
"It takes literally thousands of our residents to volunteer their time to put this on and raise money for charity organizations," he said of the garlic festival. "It's just incredibly sad and disheartening that an event that does so much good for our community has to suffer from a tragedy like this."
Josh Susong is a news director at The Arizona Republic and was formerly a journalist in the Bay Area. Follow Susong on Twitter: @jsusong


Sandvik AB (publ) operates as an engineering company in the areas of mining and rock excavation, metal cutting, and materials technology worldwide. The last earnings update was 3 days ago. More info.
SVKB outperformed the Machinery industry which returned -18.1% over the past year.
SVKB outperformed the Market in Germany which returned -6% over the past year.
Is Sandvik undervalued based on future cash flows and its price relative to the stock market?
Here we compare the current share price of Sandvik to its discounted cash flow analysis.value.
Below are the data sources, inputs and calculation used to determine the intrinsic value for Sandvik.
The calculations below outline how an intrinsic value for Sandvik is arrived at by discounting future cash flows to their present value using the 2 stage method. We try to start with analysts estimates of free cash flow, however if these are not available we use the most recent financial results. In the 1st stage we continue to grow the free cash flow over a 10 year period, with the growth rate trending towards the perpetual growth rate used in the 2nd stage. The 2nd stage assumes the company grows at a stable rate into perpetuity.
Amount off the current price Sandvik is available for.
For Sandvik to be considered undervalued it must be available for at least 20% below the current price. Less than 40% is even better.
Sandvik's share price is below the future cash flow value, but not at a moderate discount (< 20%).
Sandvik's share price is below the future cash flow value, but not at a substantial discount (< 40%).
The amount the stock market is willing to pay for Sandvik's earnings, growth and assets is considered below, and whether this is a fair price.
Are Sandvik's earnings available for a low price, and how does this compare to other companies in the same industry?
** Primary Listing of Sandvik.
Sandvik is good value based on earnings compared to the DE Machinery industry average.
Sandvik is good value based on earnings compared to the Germany market.
Does Sandvik's expected growth come at a high price?
Sandvik is poor value based on expected growth next year.
What value do investors place on Sandvik's assets?
* Primary Listing of Sandvik.
Sandvik is overvalued based on assets compared to the DE Machinery industry average.
Sandvik has a total score of 2/6, see the detailed checks below.
How is Sandvik expected to perform in the next 1 to 3 years based on estimates from 19 analysts?
Is Sandvik expected to grow at an attractive rate?
Sandvik's earnings growth is expected to exceed the low risk savings rate of 0.2%.
Sandvik's earnings growth is positive but not above the Germany market average.
Sandvik's revenue growth is positive but not above the Germany market average.
Sandvik's earnings are expected to grow by 4.8% yearly, however this is not considered high growth (20% yearly).
Sandvik's revenue is expected to grow by 2.7% yearly, however this is not considered high growth (20% yearly).
All data from Sandvik Company Filings, last reported 3 weeks ago, and in Trailing twelve months (TTM) annual period rather than quarterly.
Sandvik is not expected to efficiently use shareholders' funds in the future (Return on Equity less than 20%).
Sandvik has a total score of 1/6, see the detailed checks below.
How has Sandvik performed over the past 5 years?
Below we compare Sandvik's growth in the last year to its industry (Machinery).
Sandvik has delivered over 20% year on year earnings growth in the past 5 years.
Sandvik's 1-year earnings growth is negative, it can't be compared to the 5-year average.
Sandvik's 1-year earnings growth is negative, it can't be compared to the DE Machinery industry average.
Sandvik's revenue and profit over the past 5 years is shown below, any years where they have experienced a loss will show up in red.
Sandvik has efficiently used shareholders' funds last year (Return on Equity greater than 20%).
Sandvik used its assets more efficiently than the DE Machinery industry average last year based on Return on Assets.
Sandvik has significantly improved its use of capital last year versus 3 years ago (Return on Capital Employed).
Sandvik has a total score of 4/6, see the detailed checks below.
How is Sandvik's financial health and their level of debt?
The boxes below represent the relative size of what makes up Sandvik's finances.
Sandvik is able to meet its short term (1 year) commitments with its holdings of cash and other short term assets.
Sandvik's cash and other short term assets cover its long term commitments.
This treemap shows a more detailed breakdown of Sandvik's finances. If any of them are yellow this indicates they may be out of proportion and red means they relate to one of the checks below.
All data from Sandvik Company Filings, last reported 3 weeks ago.
Sandvik's level of debt (52.7%) compared to net worth is high (greater than 40%).
The level of debt compared to net worth has been reduced over the past 5 years (95.8% vs 52.7% today).
Sandvik has a total score of 5/6, see the detailed checks below.
What is Sandvik's current dividend yield, its reliability and sustainability?
Current annual income from Sandvik dividends. Estimated to be 2.8% next year.
If you bought €2,000 of Sandvik shares you are expected to receive €48 in your first year as a dividend.
Sandvik's pays a higher dividend yield than the bottom 25% of dividend payers in Germany (1.43%).
Sandvik's dividend is below the markets top 25% of dividend payers in Germany (3.71%).
Purchase Sandvik before the 'Buy Limit' to receive their next dividend payment.
What portion of Sandvik's earnings are paid to the shareholders as a dividend.
What is the CEO of Sandvik's salary, the management and board of directors tenure and is there insider trading?
Mr. Björn Klas Otto Rosengren, M.Sc. (Tech.), has been the Chief Executive Officer and President at Sandvik AB since November 1, 2015. Mr. Rosengren served as the Chief Executive Officer, President and a Member of Management Board at Wärtsilä Oyj Abp from September 01, 2011 to October 31, 2015. He served as a Business Area President of Construction & Mining Technique at Atlas Copco Prime Energy, LLC. He served as a Business Area President of Construction and Mining Technique at Atlas Copco North America LLC. He served as a Senior Executive Vice President and Business Area President of Construction and Mining Technique at Atlas Copco AB of Atlas Copco (India) Limited and Atlas Copco North America LLC until September 2011. He served as Business Area Executive for Construction and Mining Technique at Atlas Copco AB. Mr. Rosengren was employed by Atlas Copco AB since 1998 until 2011. From 1985 to 1995, he held various positions within Esab Group, including international assignments as Marketing Manager in Switzerland and Sweden and other international positions in the field of Marketing. He served as General Manager of Nordhydraulic, Nordwin AB and Kramfors Sweden since 1995 until 1998. In 1998, he joined Atlas Copco as President of Craelius Division and prior to that, he served as its President of Rock Drilling Equipment Division. He serves as a Board Member at HTC AB. He has been an Independent Director of Danfoss A/S since 2010 and has been its Vice Chairman since June 2, 2016. He has been a Director of Sandvik AB since April 28, 2016. He serves as a Director of Dynapac AB and Danfoss District Energy A/S. He serves as a Director of Moderna Försäkringar Sak AB. He served as a Director of Höganäs AB (publ) since May 3, 2011. He served as Director of Outotec Oyj from March 31, 2014 to September 18, 2015. He served as a Director of Pergo AB from April 2002 to April 2005. He served as a Director at Moderna Forsakringar Sak AB. He served as a Non Executive Director of Atlas Copco (India) Limited until October 2009. Mr. Rosengren holds an M.Sc. in Technology from Chalmers University of Technology, Gothenburg, Sweden in 1985.
Björn Klas's compensation has been consistent with company performance over the past year.
Björn Klas's remuneration is about average for companies of similar size in Germany.
The tenure for the Sandvik management team is about average.
The tenure for the Sandvik board of directors is about average.
Sandvik has a total score of 0/6, this is not included on the snowflake, see the detailed checks below.


After three and a half months at sea working a fishing vessel I am pleased to report that I am back on dry ground. It's been a long summer and tons of hard work, fun and quick sleep. I look forward to putting together my experiences and getting this blog back on a regular schedule. I have some great photos and unbelievable stories coming from the Prince William Sound's 2010 salmon season (and for a few of you some actual salmon), but before we get to all of that let me give you the down low on what's up.
First, while at sea I didn't have access to update the conglomorate of open source software that makes freewheelings.com possible and an outdated software package allowed unauthorized access to a file known as the .htaccess file. This redirected all visitors coming from search engines organically to a malware related site. My regular visitors, this didn't affect you at all, but probably cost me a truckload of new readers. If you got an attack page warning from Google or Mozilla when trying to open my site – That's why. It's all cleaned up now, but lesson learned. If you can't update your own software for whatever reason have someone do it for you. You'd think of all people I would know that.
Well, what comes next? I'm leaving manana and will be New Mexico bound. After buying a truck to make the drive and various expenses I have enough to make it home and work on my timber frame house outside of Taos. Or maybe just enough to make it home. Either way, I'm once again jumping into the great unknown. At least this time it will be in a familiar place with familiar faces. This will be my third time landing in New Mexico with meager means and hopes. In the past she has always taken care that I am well. Here's to hoping.
Glad see you back and can't wait to catch up with you back in NM. So does this mean that you have abandoned your "Magic" VW Bus?
It is a mixed day. Happy to hear you will come back to NM and pay us a visit. Sad to hear of the end of the line for the bus. Hopefully it will have many productive years in the great white north with new owners.
Hey now, let's not jump to conclusions. :-) See photo update above ^ The bus is still kicking AND coming home to NM. She's actually in pretty good running shape. I just would like to get home sometime this year and not have to deal with, well, you know, traveling 4,000 miles in the bus.
Dude….. 1st NM beer's on me!
You bet, but it looks like I'm going to be hanging off another week on account of having a rider to Colorado to split travel expenses. I should be home by the first.
Be careful boy pup. You'll be able to smell the green chili from the border, I'm sure!


text:
Catholic priest urges Nigerians to vote for Peter Obi
By Gbenga Adedayo
A Catholic priest, Professor Francis Ishola Ogunmodede, has advised Nigerians to vote for Peter Obi, if they are desirous to end the country's current socio-economic woes which have brought hardship to many families. Peter Obi is one of the presidential aspirants of the People's Democratic Party (PDP).
Ogunmodede who is the Episcopal Vicar of Lekki Region of the Catholic Archdiocese of Lagos, made this remark over the weekend during his visit to the Catholic Church of the Lord's Baptism, Osopa, an outstation of Catholic Church of Divine Mercy, Lekki.
According to him, his choice of Peter Obi is informed by his track records as former Governor of Anambra State where he demonstrated high level of administrative capacity and economic prudence that transformed the once troubled deficit state into surplus, saying that Nigeria needs such a person to rescue the country at this critical time.
Besides, he added that for purposes of equity and justice, it is advised a candidate from the South Eastern part of the country be given an opportunity to produce the next president, since other geo-political zones have had their own share of the presidency.
Ogunmodede who is also a Monsignor, further advise members of the church to show more commitment to God and embrace those virtues upon which the Word of God and the Eucharist are founded as part of ways to attract God's grace and love to our lives.
Specifically, he urged members to pay attention to the family, particularly, the children so that they can be brought up under good moral values, devoid of peer pressure and distraction capable of interfering with their service to God and man.
He added that since school plays pivotal role in shaping children's behaviour, it is advised they are enrolled in good schools with high ethical standards, saying, this was the essence of Catholic schools, and advised parents to patronize them.
The Episcopal Vicar also commended the growth of the Catholic Church of the Lord's Baptism, and encourage them to expand further by acquiring some of the vacant plots of land by the church to build schools and place of learning where children can be decently trained and brought up in the ways of the Lord.
The Episcopal Vicar was accompanied on the trip by Monsignor Paschal Nwazeapu and two other priests from the Catholic Church of Divine Mercy, Lekki.
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