text:
WWolfeld@hmbay.com
Warren's clients include both large and small domestic and global businesses seeking to manage, own and fortify patents and patent portfolios. Warren is dedicated to safeguarding even the most complex technologies. In his third decade of practice, Warren strives to serve each client's best interest by focusing on maximizing their opportunities and identifying and navigating beyond inherent threats and obstacles. Because Warren is able to delve deeply into new technologies, he can quickly comprehend and effectively prosecute even the most complicated and cutting-edge innovations of today. Warren is frequently complimented on his grasp of new technologies.
Warren espouses a market-driven approach to patent drafting, seeking to capture the market segment that the invention addresses. He believes that the best patents often are ones that ensure that only his client is able to make a marketing claim that is of value to customers. He is appreciated for executing precision and high-quality legal counsel both on time and on budget, and his direct communication style and vigilance for his clients' interests have created relationships of trust with many clients over the years.
Warren is truly dedicated to serving as a trusted advisor and strategic partner, and is known not only for his legal and technical prowess, but also for his often fresh perspective and out-of-the-box thinking when navigating beyond obstacles and solving the problems his clients regularly encounter. Warren's patent litigation experience early in his career distinguishes him from other patent practitioners, and has helped him to prepare and prosecute patent applications that have successfully survived punishing litigation and brought significant rewards for his clients.
Warren is involved in analyzing, drafting and prosecuting patents and patent applications, as well as in strategic portfolio management, rendering opinions, assisting in design-around efforts, and conducting due diligence studies. He advises clients in a variety of electrical and electronics-related fields, a sampling of which includes computer architectures, telecommunications hardware and software, semiconductor design, digital signal processing, microwave test instruments, discrete and integrated electronic circuitry, integrated optics, flat panel display technologies, computer software and object- and agent-oriented design, database software, speech and language processing, computer aided semiconductor design tools, superconducting electronics, neural networks, and image and video compression.
Warren is distinguished by Martindale-Hubbell as AV Preeminent. He holds a B.S. in Electrical Engineering, Magna Cum Laude, from the University of Rochester, as well as a J.D. from Cornell Law School, where he was Senior Editor of the Cornell International Law Journal. Warren is admitted to practice in both California and New York, as well as before the U.S. Patent and Trademark Office, the Court of Appeals for the Federal Circuit, U.S. District Courts for the Southern and Eastern Districts of New York, and the U.S. District Court for the Northern District of California. Warren is a member of Tau Beta Pi, IEEE, the American Bar Association, American Intellectual Property Law Association, and the San Mateo County Bar Association.
Prior to joining HBW as a Partner in 2001, Warren served as a Partner at Fliesler, Dubb, Meyer & Lovejoy LLP in San Francisco, and before that as an Associate at Kenyon & Kenyon in New York. In addition, Warren authored "International Patent Cooperation: The Next Step," published in the Cornell International Law Journal as a study of the international patent system, which was also reprinted in the Modern Legal Systems Cyclopedia and in Intellectual Property Policy and International Negotiation.
Litigation Percentage
20% of Practice Devoted to Litigation
Certified Legal Specialties
Registered Patent Attorney, United States Patent and Trademark Office
U.S. Court of Appeals Federal Circuit, 1984
U.S. District Court Southern District of New York, 1984
U.S. Patent and Trademark Office, 1984
Cornell Law School, Ithaca, New York
J.D. – 1983
Law Journal: Cornell International Law Journal, Senior Editor
University of Rochester, Rochester, New York
B.S.E.E., Bachelor of Science Electrical Engineering magna cum laude – 1980
International Patent Cooperation: The Next Step, 16 Cornell International Law Journal 229, (1983) (a study of the present and future international patent system), reprinted in 4 K. Redden, Modern Legal Systems Cyclopedia 639 (1984), and in 1 B. Dameron, Intellectual Property Policy and International Negotiation 305 (1987)
Boots Laboratories, Inc. v. Burroughs Wellcome Co. v. Boots Company , Inc., Boots Holdings, Inc., Boots Pharmaceuticals, Inc., 1984 WL 15504 (E.D.Va. 1984)
Advanced Micro Devices, Inc. vs. Samsung Semiconductor, Gazelle Microelectronics, Atmel Corporation and Cypress Semiconductor
Wiltron Co. vs. Hewlett-Packard Co.
Tandy Corporation vs. Adaptec Inc.
In re: Certain Dynamic Random Access Memories (U.S. International Trade Commission action, Texas Instruments vs. eight DRAM manufacturers)
Martindale-Hubbell of AV-Preeminent
IEEE, 1980 – Present
American Bar Association, 1983 – Present
American Intellectual Property Law Association, 1983 – Present
San Mateo County Bar Association
Fliesler, Dubb, Meyer & Lovejoy LLP, San Francisco, Partner, 1986 – 2001
Kenyon & Kenyon, New York, Associate, 1983 – 1986
Tau Beta Pi


text:
Q: Using Ghostscript in server mode to convert PDFs to PNGs while i am able to convert a specific page of a PDF to a PNG like so:
gs \
  -dSAFER \
  -dBATCH \
  -dNOPAUSE \
  -sDEVICE=png16m \
  -dGraphicsAlphaBits=4 \
  -sOutputFile=gymnastics-20.png \
  -dFirstPage=20 \
  -dLastPage=20 \
   gymnastics.pdf

i am wondering if i can somehow use ghostscript's JOBSERVER mode to process several conversions without having to incur the cost of starting up ghostscript each time.
from: http://pages.cs.wisc.edu/~ghost/doc/svn/Use.htm

-dJOBSERVER

Define \004 (^D) to start a new encapsulated job used for compatibility with Adobe PS Interpreters that ordinarily run under a job server. The -dNOOUTERSAVE switch is ignored if -dJOBSERVER is specified since job servers always execute the input PostScript under a save level, although the exitserver operator can be used to escape from the encapsulated job and execute as if the -dNOOUTERSAVE was specified.
This also requires that the input be from stdin, otherwise an error will result   (Error: /invalidrestore in --restore--).
Example usage is:
   gs ... -dJOBSERVER - < inputfile.ps
                -or-
   cat inputfile.ps | gs ... -dJOBSERVER -

Note: The ^D does not result in an end-of-file action on stdin as it may on some PostScript printers that rely on TBCP (Tagged Binary Communication Protocol) to cause an out-of-band ^D to signal EOF in a stream input data. This means that direct file actions on stdin such as flushfile and closefile will affect processing of data beyond the ^D in the stream.

the idea is to run ghostscript in-process. the script would receive a request for a particular page of a pdf and would use ghostscript to generate the specified image. i'd rather not start up a new ghostscript process every time.

A: So why can't you simply use a command like this:
gs \
  -sDEVICE=png16m \
  -dGraphicsAlphaBits=4 \
  -o pngimages_%03d.png \
   \
  -dFirstPage=20 \
  -dLastPage=20 \
   gymnastics.pdf
   \
  -dFirstPage=3 \
  -dLastPage=3 \
   sports.pdf
   \
  -dFirstPage=33 \
  -dLastPage=33 \
   athletics.pdf
   \
  -dFirstPage=4 \
  -dLastPage=4 \
   lazyness.pdf

This will generate several PNG images from different PDFs in a single go.

redpajama_set_name: RedPajamaStackExchange


About me? I'm a mother of a 10 and 5 year old, 2 daughters! When I'm not busy being mum I play video games, watch a lot of sci-fi and trawl through silly cat videos.
I have my own little shop, Fairy Fountain Gift Shop!
Most of my items are inspired by either things I'm interested in or my two daughters! We all wear the things I make, they love to help give me ideas for what they and their friends would like!
Alexandrite & Moissanite Diamond 9ct, 14k or 18ct solid Gold and 925 Silver Colour Change Engagement ring.
A5 Notebook. Magic Of The North. Reindeer And Aurora Borealis. Spiral Bound A5/C5 size/Plain Pages.


Kevin Armentrout is a United States Marine Corps combat veteran and recipient of the Bronze Star medal for valor. As an expert in small unit leadership, Kevin specializes in providing personal and corporate leadership training. He has made a lasting impact on so many as a published author, personal development coach, and public speaker. He has traveled around the world as a keynote speaker and is a reoccurring guest for the #1 Life and Business Strategist, Tony Robbins.


5G-Xcast is proud to announce that deliverable D3.2 on Air Interface is now released and can be downloaded from this link.
This report investigates the 3GPP Release'15 (Rel'15) of 5G New Radio (NR), and extends the air interface to point-to-multipoint (PTM) communications. Two specific 5G PTM technologies are proposed in order to fulfil the different 3GPP requirements needed for broadcast and multicast, as well as those derived from the 5G-Xcast use cases defined in Deliverable D2.1. These technologies are the Mixed Mode and the Terrestrial Broadcast Mode. 5G-Xcast partners have been contributing to the 3GPP Rel'16 discussions in order to detect missing functionalities that are needed to fulfill the agreed PTM requirements.
The 5G-Xcast Mixed Mode enables a dynamic and seamless switching between Point-to-Point (PTP) and PTM transmissions both in the downlink and the uplink. This solution is envisaged for the different verticals of the 5G-Xcast project, i.e. media and entertainment, automotive, internet of things (IoT) and public warning. It reuses the NR Rel'15 air interface specification as much as possible to ensure the maximum compatibility with PTP. However, some modifications are included such as the discovery of the scheduling information to a group of users is enabled by the introduction of a Group Radio Network Identifier (G-RNTI), and a multiple cell coordination that is enabled by forcing the same cell scrambling sequence to the neighbouring Next Generation NodeBs (gNB). Negative numerologies as well as the concept of mini-slots are also included to support SFN areas and larger deployments.
The 5G-Xcast Terrestrial Broadcast Mode enables the reception of the service to users without uplink capabilities, i.e. being a downlink-only mode. One of its design principles is the transmission over large coverage areas in order to enable the media delivery through deployments including High-Power High-Tower (HPHT) network configurations. To make this possible, a new physical channel has been defined. It includes new cyclic-prefix values and reference signals, as well as a Cell Acquisition Subframe (CAS) and a very narrow carrier spacing (even more than those provided in the Mixed Mode) in the frame structure to allow very large Inter-Site Distances (ISDs) in Single Frequency Networks (SFNs), as required by the 3GPP requirements.
This deliverable also provides an evaluation of the 5G NR Rel'15 unicast specifications against specific Key Performance Indicators (KPIs), as defined in the IMT-2020 guidelines. It includes analysis, inspection and link-level simulations. In addition, the two 5G-Xcast PTM solutions are evaluated in order to demonstrate the more efficient use of the radio resources and their advantages over PTP for the scenarios considered in 5G-Xcast.


Or just call us on 0800 LOSTPET to ask us directly.
What does it cost to Register my pet?
There is a one-off registration fee of $15 (RRP), inclusive of GST. This fee is for the life of the animal. This is paid to your vet at time of implantation/verification along with the cost of the microchip, the cost of the implant and /or the administration fees charged by your vet, spca or implanter. The total cost may vary so ask your vet or implanter for more information and pricing.
My pet is already microchipped, can I still enter my pet in the NZ Companion Animal Register?
Absolutely! Either visit your vet and ask them to complete the NZ Companion Animal Register Application Form on your behalf, or call Animal Register Limited on 0800 LOST PET (567873), during office hours, and we can explain the process of registration. You will be required to provide proof of ownership and proof of microchip BEFORE your records will be entered.
My dog is already microchipped and is registered with my local council. Do I still need to register on the New Zealand Companion Animal Register?
Yes you do. The National Database that local councils (Territorial Authorities) use was intended for dog control purposes and was never designed for the retrieval of lost pets. The New Zealand Companion Animal Register is designed specifically to make the recovery of lost pets easier by ensuring that anyone can quickly check to see that your microchip number is on the database and important agencies involved with lost and or injured pets can access the database quickly and efficiently to search for that animal's owners and carers. Importantly, the register has been established by organisations deeply interested in Animal Welfare. Funds received from your registration fee will be used and reinvested in projects to help animals particularly in the area of animal welfare.
Microchips are a small device about the size of a grain of rice. The microchip is implanted in the soft scruff of the neck. The microchip has a unique number that can be read by a special reader, similar to a barcode reader. This number is stored in our register with your contact details. The microchip does not include a GPS (Global Positioning System).
Placing a microchip is a common procedure and safe for your animal. We strongly recommend that your animal is microchipped by a Vet or someone experienced in the procedure to ensure the microchip is implanted correctly.
Our web site is available 24/7 and this allows authorised agents to search and recover owner details at any time, as well as allowing owners to update details online at any time. We also have our 0800 LOST PET (567873) support number which is manned 8.30am until 5.00pm Monday to Friday. Messages can be left on the 0800 number outside of these hours. You can also email Animal Register Limited at info@animalregister.co.nz and you will receive a reply within 1 working day.
What will it cost to recover my pet when it is lost?
There is no charge for the release of details in the New Zealand Companion Animal Register. All such use is covered by the initial registration fee.
If your email details are on your registration then you can request online access to your records to allow you to update them for no charge. Just go to UPDATING YOUR CONTACT DETAILS, and follow the instructions. Alternatively you can contact Animal Register Limited during normal office hours and arrange to update your details manually.
If my dog is in the New Zealand Companion Animal Register, do I need to register my dog with my local council?
Definitely. Dog registration with your local council is a legal requirement and different to our animal repatriation database.
Where can I get my animal microchipped?
Microchipping can be done by any Vet, Vet Clinic, SPCA as well as some breeders and other animal welfare organisations. Click here to see a list of New Zealand vets and SPCA's to find the one nearest you.
What do I do if I have lost my pet or found a pet?
There are a number of steps you can take when you have lost your pet. Please click here for some helpful steps. You can also create your own lost pet posters. If your animal is found and taken to a vet, SPCA or pound it will be scanned and the microchip number can be entered on our database to retrieve any details recorded.
Can I microchip my own animal and enter it into the database?
The Companion Animal Register only accepts registrations from approved animal entry officers. These are normally Vet Clinics and SPCA's. Some breeders are also approved officers, but it is not anticipated individual owners will be. Any individual would need to take their animal to an approved officer so the microchip number can be verified and the approved form completed.
Can I register other types of animals in the Companion Animal Register?
The register will accept registration of a variety of animals into the database. This may include Birds, Reptiles, Cows, Deer, Emu, Goats, Horses, Llamas, Alpacas, Ostrich's, Rabbits, Guinea Pigs, Sheep as well as Cats and Dogs.
My pet has passed away, who should I tell?
The passing of your loved pet is a difficult time and your first thoughts should always be supporting the family. In the first instance your vet clinic, or usually any vet clinic if you have moved, can help with looking after your pet until you are ready to make any decisions. Many clinics can also assist with advice on next steps too. If registered on the NZCAR, you are able to notify us by email or phone and we will update your pets records to ensure you receive no more emails regarding updating contact details. If the passed pet is a dog and registered, then we would also recommend advising your local Council too.


"Dad drinks beer every evening."
Translation:Baba anakunywa bia kila jioni.
I learned that ku- is always leaving in the present as Long as the word has more than one syllable. So here it should be: Baba ananywa bia kila jioni. Because ku- ny-wa has 2 syllables.
You are correct that ku- (the prefix) leaves. But ku- is not the prefix in this word. It would not be correct to say "kuanakunywa" because when conjugating the verb, we remove the infinitive prefix like you say.
Noah: your 'explanation' is incorrect.
The stem -nywa is one syllable, therefore the ku- remains in the present tense. The y in is this letter combination is a consonant, and pronounced as the the Y in New York. And not as in by.


text:
Q: HIGHSLIDE JS : fixed position of the gallery I'm using Highslide for show some images on my website.
Look here to know what I'm using : http://highslide.com
I use autoloading because I want just see the popup without the gallery. It seems to work fine. But I want it to stay in the same place no matter where I am in the page.
How can I fix the popup of my highslide galery (like a div in a relative position) ?
I try it with targetX & targetY elements but that works just when I load the page; when I click on an other image, the popup "follows" the size of the page.
My site is not online but check my code here :
In the head of my page :

<link rel="stylesheet" type="text/css" href="<?php echo "http://".CHEMIN_HIGHSLIDE."highslide.css"; ?>" />

<title>Titre</title>

In the body :

            header

                //target for the place of highslide gallery in the page

            <?php
                //array of images to show (I keep it otherwhere)
                $array=array(
                    array('nom'=>'image 1','lien'=>'link_img_1','txt'=>'Text sup image 1'),
                    array('nom'=>'image 2','lien'=>'link_img_2','txt'=>'Text sup image 2'),
                    array('nom'=>'image 3','lien'=>'link_img_3','txt'=>'Text sup image 3')
                );
                //...
                if(isset($array))
                {
                    $nb=sizeof($array);

                    $i=1;
                    //HIDDING THUMBNAILS
                    echo '
';
                        foreach($array as $arr)
                        {
                            echo '

                                    '.$arr['txt'].'
                                  ';
                            $i++;
                        }
                    echo '
';
                }
            ?>

            footer

I really searched the internet. I found some things, but everything is in English, and although I do understand a little, there are many things I do not understand.
I have also seen such a function to be integrated so that targetX & targetY work but I really do not know where.
onclick = "return hs.htmlExpand (this, {contentId: 'highslide-html' targetX: null, targetY 'target 0px', height: 700, width: 480})"

May anyone help me please?

A: I believe the "in-page gallery" examples on this page will get you steered in the right direction:
http://www.roadrash.no/?page_id=11


Portrait of Marston Sargent (1906-1986), who was associated with Scripps Institution of Oceanography for more than 40 years. During which time he primarily investigated photosynthesis and the growth requirements of marine planktonic algae. He also served as the CalCOFI Coordinator from 1971-74. Under his guidance, CalCOFI began its longstanding and fruitful relationship with Mexico. Circa 1935.
Richard Howell Fleming, a chemist at the Scripps Institution of Oceanography and one of the three authors of the landmark 1942 text and reference, "The Oceans: Their Physics, Chemistry and General Biology", is depicted here aboard Scripps research vessel, R/V Scripps. August 1, 1935.
Richard Howell Fleming, a chemist at the Scripps Institution of Oceanography and one of the three authors of the landmark 1942 text and reference, "The Oceans: Their Physics, Chemistry and General Biology", is depicted here aboard Scripps research vessel, R/V Scripps. Circa 1935.
Robert S. (Robert Sinclair) Dietz, posing on car while at Scripps Institution of Oceanography, he was a geophysicist and oceanographer, while at the Institution he observed the nature of the Emperor chain of seamounts. Circa 1938.
Roger Revelle (1909-1991), at drafting table. Circa 1936.
Roger Revelle (left) and Richard Howell Fleming during coring operations aboard the Scripps Institution of Oceanography research vessel, R/V Scripps. September 23, 1935. Richard Howell Fleming was a chemist at the Scripps Institution of Oceanography and one of the three authors of the landmark 1942 text and reference, "The Oceans: Their Physics, Chemistry and General Biology". Sepember 23, 1935.
Roger Revelle with specimens on the deck of the Scripps Institution of Oceanography research vessel, E.W. Scripps. Circa 1936.


text:
Challenge Poverty Week - Belville Community Garden
We've had a chat with Sally Clough, manager at Belville Community Garden, to discover the organisation's incredible work in our communities to support vulnerable people
What services and resources do you offer to tackle poverty?
Our services and resources really revolve around food provision. However, we operate a lot on emergency food provision which is something we're trying to move away from because there's no impetus for people to improve their long-term goals for their futures when we're just handing them bags of food. So we're looking at developing projects where we're delivering a lot more than the food – it's the information and the knowledge and what to do with it and where to source it.
There are things we can do that suit both long term sustainability in Inverclyde and also reduce the cots of living. The perception, and certainly my own perception, of a lot of environmental initiatives (like zero waste shops) is that you end up paying more: if something's green then it's going to cost you more and that's just the way it is. That's why a lot of the time we don't buy the green products, we buy the things covered in plastic because we can't afford to pick that environmentally sustainable product.
What role does your community garden play?
The food we provide is not always food we grow in the garden, we don't have a high level of production from the garden. Our garden is more about teaching people, getting people out there and helping them improve their mental health and getting them active in the community. Everything we grow is a bonus!
We have a lot of environmental initiatives. For example, we pick up the food waste from supermarkets and we distribute that as community food. We were part of a 2 year project with the Climate Challenge Fund where we collected over 80,000 kilograms of food and we developed a system of community fridge-freezers we had all over Inverclyde, but with Covid hitting this evolved into food shares which is an Inverclyde project where there are five food shares in Inverclyde. We've outsourced the supermarket collections to different people and it's still getting collected and going to the community, it's just been spread out more and more people are getting involved.
We offer work skills and training to get people work-ready which is another route to tackling poverty.
What is the best way for people to access your services?
Contacting us. We also have a lot of organisations that are familiar with us who will refer people to us. But really all you need to do is pick up the phone and give us a call.
That's a challenge for some people. You can come through community link workers, SMAH, all sorts of different routes.
What impact has your organisation made to challenge poverty in Inverclyde?
Certainly not solved it! It's an ongoing fight and if we weren't in somebody else would've had to step up and be in it. It's really just about keeping that fight going, raising the awareness that some people don't have; it's not easy for some people, you can't judge people, we need to get stigma out of the way. It could be you tomorrow. It's really just about attitude and challenging stigma.
Our main issue is reaching people. We have a lot of activity going on and we have a lot of clients but there's people that we know we're not getting to.
How important is it that we challenge poverty in Inverclyde?
Why wouldn't it be important. Inverclyde has high levels of poverty and deprivation and we can see the impact tat has on mental health, on drug and alcohol abuse, on crime rates, childhood trauma – the list is endless. If we could eridicate poverty, and just take a step up the ladder, everybody has a little more breathing space.
How important is it that we tackle stigma associated with poverty?
Stigma is a really difficult one and as soon as you start talking about poverty and targeting people to speak about it you're increasing that stigma.
There isn't anything to feel bad about. It could be me tomorrow.
Personally, I don't think we can tackle poverty until we have the correct social services in place to support that in the background. Unless you're helping people with their issues then something like the emergency food provision doesn't help in the long term. So there's a lot of long-term solutions that need to be put in place if this is to ever be tackled.
➡ Find out more about Belville Community Garden and view their Inverclyde Life's directory - click here.
Chris Park

redpajama_set_name: RedPajamaCommonCrawl


text:
If Durham doesn't build more housing, she said, "we will become even more unaffordable than we already are."
The council's five-year housing plan aims to:
▪ Preserve and expand affordable rental units and rental assistance, with a focus on households under 50 percent of the average median income (AMI).
▪ Maintain affordability and protect very low-income households in neighborhoods experiencing significant housing cost increases.
▪ Engage the larger Durham community to make affordable housing a citywide priority.
To be affordable, experts say housing should not exceed 30 percent of gross income.
In Durham in 2012, there were 19,500 low-income renters paying more than that. That's 42 percent of all renters.
That same year, 7,800 low-income owners were paying more than 30 percent of their income on housing. That's 15 percent of all owners. Both measures of "low income" were less than 80 percent of the average median income.
According to U.S. Census data, the median household income in Durham from 2012-16 was $54,000.
Mayor Steve Schewel noted the council approved townhome projects in recent meetings but often gets pressure from existing neighborhoods not to add density.
"There are fewer forces more powerful than a single-family neighborhood, half of whom are our friends, trying to stop neighborhoods around them," Schewel said.
Freeman said it's often "non-people of color" trying to stop new housing and that more housing that is affordable needs to be built.
Schewel said the people he hears from most are middle-class people who can't afford to buy in places like Old West Durham and Northgate Park and want the city to help them.
The city's housing plan does not target housing for them, but rather those most in need who are living in Durham Housing Authority properties. The city has finite resources, Schewel said.
Community Development's presentation pointed out that the highest median home values are downtown and in Southwest Durham. The lowest are in East Durham.
The council did not take any action at its meeting, but talked in general about moving forward with policy goals.
For the 2018-19 fiscal year, the goals include:
▪ Plan and first phase of financing in place to redevelop Durham Housing Authority downtown properties; 356 DHA units rehabilitated at three existing properties.
▪ Over 230 rental and for sale units completed or in process (new and preserved).
▪ Over 40 owner-occupied units repaired or rehabilitated.
▪ New tools – housing trust fund, affordable housing incentives, revised Unified Development Ordinance.
▪ New partnerships – city departments, GoTriangle, private and community organizations.
Just because the council isn't spending its money on the middle class doesn't mean it isn't going to try to help.
Schewel that a way to address the "missing middle," a phrase used to describe middle-class needs, is accessory dwelling units.
Planning Director Pat Young said that post-World War II zoning is a significant contributor to the housing problem today. Previous zoning protected the natural environment and managed community character, but at a very high cost, Young said. So the planning department is meeting with smaller developers to look at expanding housing choices like small homes and "micro units." They'll roll out a plan to the community in the spring, he said.
Dawn Baumgartner Vaughan: 919-419-6563, @dawnbvaughan
Video released in shooting of Ondrae Hutchinson in Durham
Durham County investigating possible measles case
A haunting photo of a large snake that died struggling to free itself from a maze of netting has come to illustrate a growing problem of discarded plastics at North Carolina lakes and beaches
MORE DURHAM COUNTY
Mother of slain Durham teen wants justice in unsolved murder
'Way across the line.' UNC system board to examine redevelopment program.
Durham needs affordable housing downtown. Here's where it's happening.
Dozens of shell casings found outside Durham home where girl was shot, boy injured
Family of dead man says DA went too easy on shooter of Durham father of 4
2 men died in a botched beer robbery. Cousins now sentenced in store clerk's murder.


The mission of The Smoky Mountains Songwriters Festival is to provide an amazing setting and opportunity for songwriters, music professionals and music lovers to come together and enjoy, learn, share, and preserve the craft of songwriting.
There is a song in everyone….. We welcome the Public as well as songwriters to participate in any facet of the festival they would like to attend.
Sun Aug 11-14, 2019 SMSWF Bluegrass Camp.
Mon Aug 12, 2019 2nd Monday SMSWF Songwriters Showcase Reunion at Crystelle Creek Restaurant & Grill (1654 E. Parkway) hosted by John Condrone.
Wed Aug 14, 2019 Bobby Tomberlin & Friends at Crystelle Creek Restaurant & Grill (1654 E. Parkway) 7 pm till?
Weds/Thurs Aug 14-15, 2019 SMSWF Rocky Top Co-write with Hit Writers Experience Click here for details and to register for the Co-Write at the Festival.
Thurs Aug. 15, 2019 SMSWF Workshops Start 1:00 – 3PM & 3:30 – 5:30. Click here for details on the workshops and to register.
Thurs Aug. 15, 2019 Welcome Ceremonies & Kick Off Show on the lawn at the Historic Gatlinburg Inn. Welcome Ceremonies start at 7:00 PM. Public Welcome. There will be chairs on the lawn but feel free to bring your own so you know you get a seat.
Sun Aug 18 Gospel Sunday 9:30-2:00 PM on the at the Historic Gatlinburg Inn (755 Parkway).


Optional Props: Name cards attached to players to identify them, a crown for the King, a staff for Joshua, binoculars or a magnifying glass for the spies, a shawl for Rahab, a piece of red yarn for Rahab (to be kept in her pocket till the appropriate time), swords for the soldiers of Jericho, a sign that says "Rooftop," and one that says "Window." Place the rooftop sign on a tabletop, and the window sign on the back of a chair.
Cast: Teacher/narrator, Joshua, two children to be the Israelite spies, Rahab, King of Jericho, and two children to be soldiers of Jericho. You may want the children to rehearse the skit before the lesson, or perform it impromptu.
Narrator: The Bible tells us that Moses and the Israelites wandered in the desert without reaching the Promise land for 40 years. After Moses died God told Joshua that he would become the new leader to fulfill God's promise to his people, and he would lead them into the Promised Land.
So Joshua assembled the Israelites, and told them to get ready to cross the Jordan River to take over the land. Before they took over the land, Joshua chose two spies to check out one of the most wicked cities, Jericho. There the spies entered the house of a prostitute named, Rahab. The Bible tells us that Rahab and the people of that entire region had heard about the power of the God of Israel, and that she and they were very afraid. Because Rahab feared God, she wanted to help the spies by hiding them from the King of Jericho and his soldiers.
Joshua: (speaking to the spies) "Go look over the land God promised to us, especially that wicked city, Jericho. Then tell me what you find. And remember what God said, 'Be strong and courageous because the LORD your God is with you wherever you go!'"
Spy 1: (sneaking away and finding Rahab) "Shalom, peace to you! We are hiding from your King. Will you hide us and keep us safe?"
Rahab: "I have heard miraculous stories about how your God parted the Red Sea to help you escape from Egypt, and how your God defeated all the armies that came against you. I will hide you because I want to serve your God. Come get on my rooftop and I'll cover you with this grain so no one will find you!"
King of Jericho: (speaking to his soldiers) "I have heard that the Israelites are ready to take over our land. Go hunt their spies down and kill them before they have a chance to defeat us!"
Soldier 1: (Pretending to look for the spies but do not find them) "Oh spies, where are you? If we find you, we will kill you! Come out, come out, wherever you are!"
Soldier 2: (Finds Rahab and speaks to her) "We have heard that you have helped those Israelite spies. Where are they? Tell us now!"
Rahab: "The spies were here but they left. I don't know which way they went. But if you leave now, you might catch them!"
Rahab: "You-hoooo...spies...the coast is clear. Come out; it's safe!"
Spy 2: "Wow, that was close! Thank you for hiding us. We'll be going now."
Rahab: "Wait a minute! Not so fast! Since I was kind to you, please protect my family and me so we're not killed!"
Spy 1: "Your lives for our lives! If you don't tell on us, we will treat you kindly and protect you and your family when we invade Jericho and take it over."
Rahab: "Ok! Here, crawl down this rope through the window. Then run to the hills and hide there until the soldiers come back to the city. Then you will know that it is safe for you to return to your camp."
Spy 2: "As a sign of our promise to protect you, and your promise to not tell on us, when we enter the land to take it over, hang a scarlet colored cord in the window to show that you have kept your word. When we see the scarlet cord, we will know that you are on our side. God will then protect you and your family from death when Jericho is destroyed."
Spy 1: (Reports to Joshua) "It is time to take over the land. Everyone is afraid of God's army. The LORD has surely given them and the land into our hands!"
Joshua: "Let's go and conquer the land that God promised to Abraham and all our descendants."


text:
\section{Introduction}\label{S:intro}

Generations of graduate students in the mathematical sciences have wrestled to understand the Caratheodory Extension Theorem. A crucial part of any advanced Real Analysis course, the process extends an algebra to a $\sigma$-algebra and a measure on an algebra to a measure on a $\sigma$-algebra. This is a powerful tool in measure theory and statistics.

Let $\mu$ be a measure on an algebra $\Omega \subset$ $ \mathbf{P}(X)$. The Caratheodory Extension consists of the following two main definitions: Definition 1; $\mu^{\ast}$ : $\mathbf{P}(X)   \rightarrow$ $\mathbb{R}^{+}$ where $\mu^{\ast} (E)$ = $\inf \{ \sum \mu (A_{i}) \mid  E  \subseteq \cup  A_{i}$ and $A_{i}  \in \Omega$ for all i $\geq $ 1$\}$ [1].
Definition 2; E $\in \mathbf{P}(X)$ is Measurable with respect to $\mu^{\ast}$ if for every set $A$ $\in \mathbf{P}(X)$, we have $\mu^{\ast} (A)= \mu^{\ast}(A \cap E) + \mu^{\ast}(A \cap E^{\textbf{C}} )$.

In general $\mu^{\ast}$ is not a measure on $\mathbf{P}(X)$. In fact it turns out that the set $M$ of measurable sets forms a $\sigma$-algebra and that ($\mu^{\ast}$, $M$) is a measure space. Where definition 2 came from always seemed a mystery to the authors.

In this paper, we propose what we believe to be a simplification of the proof of the Caratheodory Extension Theorem when $\mu$ is $\sigma$-finite. Our first step is to define the pseudometric $d (\cdot,\cdot)$ = $\mu^{\ast} (\cdot \triangle \cdot)$. We will say a sequence $\{ B_{n} \}$ in $\Omega$ is $\mu$-Cauchy iff $\lim d ( B_{n}  , B_{m}   )  \rightarrow $ 0. Next we define $ \widetilde{\mathbf{S}}$ = $\{S \in \mathbf{P}(X)  | \exists \ \mu$-Cauchy sequence  $\{B_{n}   \}   $ s.t. $ \lim \mu^{\ast} ( B_{n}   \triangle S)  =0   \}$.

In particular, $ \widetilde{\mathbf{S}}$ merely consists of limit points of $\mu$-Cauchy sequences. The authors believe that $ \widetilde{\mathbf{S}}$ is both an intuitive and natural definition. Our $ \widetilde{\mathbf{S}}$ will replace Definition 2 in the Caratheodory Extension Theorem. For $S$ $\in \widetilde{\mathbf{S}}$, we define $\widetilde{\mu} (S) $ =  $\lim \mu ( B_{n}   )   $ where $\{ B_{n}   \}$ is a $\mu$-Cauchy sequence which converges to $S$. We will show that ($\widetilde{\mu}$, $ \widetilde{\mathbf{S}}$) is the measure space obtained by the Caratheodory Extension Theorem.

\section{Main Results}
Let $\mu$ be a finite measure on an algebra $\Omega \subset$ $ \mathbf{P}(X)$ and $\mu^{\ast}$ be the outer measure defined by $\mu^{\ast}(A)$  = $\inf \{ \sum \mu (A_{i}) \mid  E  \subseteq \cup A_{i}$ and $A_{i}  \in \Omega$ for all i $\geq $ 1$\}$ for any $A \in \mathbf{P}(X)$.

\begin{lemma}\label{L:1}
$d$ : $\mathbf{P}(X)  \times   \mathbf{P}(X)   \rightarrow$ $\mathbb{R}^{+}$ where $d(A,B)$ = $\mu^{\ast}(A \triangle B)$ is a pseudometric.
\end{lemma}

\begin{remark}\label{R:1}
$d$ is a metric on $\mathbf{P}(X)_{\diagup_{\sim} } $ where A $\sim$ B  iff   $\mu^{\ast}(A \triangle B)$ =0, [2].
\end{remark}

\begin{lemma}\label{L:2}
$d(A_{1} \cup A_{2},A_{3} \cup A_{4})$  $\leq$   $d(A_{1} , A_{3})$ +  $d(A_{2} , A_{4})$ for any $A_{i} \in  $ $\mathbf{P}(X)$ .
\end{lemma}

\begin{proof}

$d(A_{1} \cup A_{2},A_{3} \cup A_{4})$

= $\mu^{\ast} ((A_{1} \cup A_{2}) \cap (A_{3} \cup A_{4})^{\textbf{C}}  \ \cup \  (A_{3} \cup A_{4}) \cup (A_{1} \cup A_{2})^{\textbf{C}} )$

= $\mu^{\ast} (A_{1} \cap A_{3}^{\textbf{C}} \cap A_{4}^{\textbf{C}} \ \ \cup \ \ A_{2} \cap A_{3}^{\textbf{C}}  \cap A_{4}^{\textbf{C}} \ \ \cup \ \  A_{3} \cap A_{1}^{\textbf{C}} \cap A_{2}^{\textbf{C}} \ \  \cup \ \  A_{4} \cap A_{1}^{\textbf{C}}  \cap A_{2}^{\textbf{C}})$

$\leq$ $\mu^{\ast} (A_{1} \cap A_{3}^{\textbf{C}}  \ \cup  \  A_{2} \cap A_{4}^{\textbf{C}} \ \cup \ A_{3} \cap A_{1}^{\textbf{C}} \  \cup \ A_{4} \cap A_{2}^{\textbf{C}})$

$\leq$ $\mu^{\ast}(A_{1} \triangle A_{3})$ + $\mu^{\ast}(A_{2} \triangle A_{4})$ = $d(A_{1},A_{3})$ + $d(A_{2},A_{4})$.

\end{proof}

\begin{lemma}\label{L:3}
$\mu^{\ast} |_{\Omega} = \mu $, from page 292 of [1].
\end{lemma}

\begin{definition}\label{D:1}
If $B_{n} \in \Omega$, then $\{B_{n} \}$ is called a $\mu  $-Cauchy sequence if $\lim \mu(B_{n} \triangle B_{m})$ $\rightarrow$ 0 as $n,m \rightarrow \infty$.
\end{definition}

\begin{convention} Unless otherwise stated, $\{B^{\alpha}_{n} \}$ and $\{B_{n}   \}   $ will be $\mu  $-Cauchy sequences.
\end{convention}

\begin{lemma}\label{L:limit} $\{B_{n}   \}   $ a $\mu  $-Cauchy sequence implies $\{ \mu ( B_{n} ) \}$ is a Cauchy sequence of real numbers.
\end{lemma}

\begin{proof}
$ |  \mu(B_{m} ) - \mu ( B_{n} )  | $ $ \leq $  $ \mu ( B_{m} \triangle B_{m} )  $ $\rightarrow  $ 0. Thus, $\{ \mu ( B_{m}) \}$ is a Cauchy sequence in $\mathbb{R}$. Thus, the claim follows.

\end{proof}

\begin{lemma}\label{L:4}

$\{B^{\alpha}_{n} \cup  B^{\gamma}_{n} \}$ and $\{(B^{\alpha}_{n})^{\textbf{C}} \}$ are  $\mu  $-Cauchy sequences.

\end{lemma}

\begin{proof} by Lemma $\ref{L:2}$,

$d(B^{\alpha}_{n} \cup B^{\gamma}_{n},B^{\alpha}_{m} \cup B^{\gamma}_{m})$ $\leq$ $d(B^{\alpha}_{n} ,B^{\alpha}_{m} )$ + $d( B^{\gamma}_{n}, B^{\gamma}_{m})$.

Moreover, $d((B^{\alpha}_{n})^{\textbf{C}},(B^{\alpha}_{m})^{\textbf{C}})$ =  $\mu((B^{\alpha}_{n})^{\textbf{C}} \triangle (B^{\alpha}_{m})^{\textbf{C}})$

=  $\mu(B^{\alpha}_{n} \triangle B^{\alpha}_{m})$ =  $d (B^{\alpha}_{n}, B^{\alpha}_{m})$. Hence the claim follows.

\end{proof}

\begin{definition}

Let $ \widetilde{\mathbf{S}}$ = $\{S \in \mathbf{P}(X)  | \exists \ \mu$-Cauchy sequence  $\{B_{n}   \}   $ s.t. $ \lim \mu^{\ast} ( B_{n}   \triangle S)  =0   \}$

\end{definition}

\begin{lemma}\label{L:5} $ \widetilde{\mathbf{S}}$ is an algebra.
\end{lemma}

\begin{proof}
Let $S_{1} , S_{2} \in$ $ \widetilde{\mathbf{S}}$. There exist $\mu$-Cauchy sequences  $ \{ B^{1}_{n} \}$ and $ \{ B^{2}_{n} \}$ which correspond to $S_{1} $ and $ S_{2}$ respectively.

Now $ \mu^{\ast} (  S_{1} \cup S_{2}  \  \triangle \   B^{1}_{n} \cup  B^{2}_{n}    )  \leq  $ $  \mu^{\ast} (  S_{1}   \Delta    B^{1}_{n}     )      $   +  $\mu^{\ast} (  S_{2}   \Delta    B^{2}_{n}    )   $ by Lemma $\ref{L:2}$.

Thus , since $\{ B^{1}_{n} \cup  B^{2}_{n} \}$ is a $\mu$-Cauchy sequence by Lemma $\ref{L:4}$, by taking the limit on both sides,  $S_{1} \cup S_{2} \in$ $ \widetilde{\mathbf{S}}$.

In addition, this covers the finite union case. Note now that $\{ B^{1}_{n} \cup  B^{2}_{n} \}$ is a $\mu $-Cauchy sequence which corresponds to  $S_{1} \cup S_{2}$.

Similarly,  $(S_{1})^{\textbf{C}} \in$ $ \widetilde{\mathbf{S}}$, thus $ \widetilde{\mathbf{S}}$ is an algebra.

\end{proof}

\begin{definition}\label{D:2} Definition of the measure on $ \widetilde{\mathbf{S}}$.

Let $S \in$ $ \widetilde{\mathbf{S}}$. Then there exists a $\mu$-Cauchy sequence $ \{ B_{n} \}$ which corresponds to $S$. By lemma $\ref{L:limit}$, $\lim \mu ( B_{n}   )   $ exists. We define $\widetilde{\mu} (S) $ =  $\lim \mu ( B_{n}   )   $.

\begin{remark}\label{R:2} By lemmas $\ref{L:1}$ and $\ref{L:3}$, $ |  \mu^{\ast} (S ) - \mu ( B_{n} )  | $=$ |  \mu^{\ast} (S \triangle \emptyset) - \mu^{\ast} ( B_{n} \triangle \emptyset)  |   \leq $  $ \mu^{\ast} ( B_{n} \triangle S )  $ for $S$ in $ \widetilde{\mathbf{S}}$. Thus, $\widetilde{\mu} (S) $= $\lim \mu ( B_{n}   )   $ =$ \mu^{\ast} (S ) $. Hence, $\mu^{\ast}  |_{\widetilde{\mathbf{S}}} $ = $\widetilde{\mu}$.

\end{remark}
\end{definition}

\begin{lemma}\label{L:6}  If $S_{1} , S_{2}  \in$ $ \widetilde{\mathbf{S}}$ are disjoint, then $\widetilde{\mu} (S_{1} \cup S_{2} ) $ = $ \widetilde{\mu} (S_{1} )   $ + $ \widetilde{\mu} (S_{2} )   $.
\end{lemma}

\begin{proof}
Let $S_{1} , S_{2}  \in$ $ \widetilde{\mathbf{S}}$ be disjoint, then there exists $\mu$-Cauchy sequences  $ \{ B^{1}_{n} \} $ and $ \{ B^{2}_{n} \}$ which correspond to $S_{1} $ and $ S_{2}$ respectively. By Lemma $\ref{L:5}$, $ S_{1}^{\textbf{C}} \cup  S_{2}^{\textbf{C}} $ $\in \widetilde{\mathbf{S}}$ and $ \{ (B^{1}_{n})^{\textbf{C}} \cup (B^{2}_{n})^{\textbf{C}}  \} $ is a $\mu$-Cauchy sequence which corresponds to $ S_{1}^{\textbf{C}} \cup  S_{2}^{\textbf{C}} $. It follows $\lim \mu^{\ast} ( S_{1}^{\textbf{C}} \cup  S_{2}^{\textbf{C}}   \  \triangle \ (B_{n}^{1} )^{\textbf{C}} \cup   (B_{n}^{2} )^{\textbf{C}}     ) $ = 0. Note ($S_{1}^{\textbf{C}} \cup  S_{2}^{\textbf{C}}$ ) $\triangle  $  ($(B_{n}^{1} )^{\textbf{C}} \cup   (B_{n}^{2} )^{\textbf{C}}    $)= $ B_{n}^{1} \cap B_{n}^{2}  $ since $S_{1}$ and $S_{2}$ are disjoint. Now we have   $\lim \mu^{\ast} (  B_{n}^{1} \cap B_{n}^{2} ) $ = $\lim \mu (  B_{n}^{1} \cap B_{n}^{2} ) $ = 0   $\ $  (1).

Note $B^{1}_{n}$ =  $(B^{1}_{n}  \cap    B^{2}_{n})$ $\cup$  $B^{1}_{n} \cap  (B^{2}_{n})^{\textbf{C}} $  implies $\mu(B^{1}_{n})$ = $\mu( B^{1}_{n}  \cap    B^{2}_{n}) $ + $\mu( B^{1}_{n} \cap  (B^{2}_{n})^{\textbf{C}} )$ and $\lim   \mu(B^{1}_{n})$ = $\lim  \mu( B^{1}_{n} \cap  (B^{2}_{n})^{\textbf{C}} )$ by (1). Similarly, $\lim   \mu(B^{2}_{n})$ = $\lim  \mu( B^{2}_{n} \cap  (B^{1}_{n})^{\textbf{C}} )$.

Moreover, $\mu( B^{1}_{n}  \cup    B^{2}_{n})$ = $\mu( B^{1}_{n}  \cap    B^{2}_{n} \ \  \cup \ \    B^{1}_{n} \cap  (B^{2}_{n})^{\textbf{C}}    \ \ \cup  \ \  B^{2}_{n} \cap  (B^{1}_{n})^{\textbf{C}}  )$

= $\mu( B^{1}_{n}  \cap    B^{2}_{n} )$ +    $\mu (B^{1}_{n} \cap  (B^{2}_{n})^{\textbf{C}}) $ +  $\mu (B^{2}_{n} \cap  (B^{1}_{n})^{\textbf{C}}  )$. Thus, $\widetilde{\mu} (S_{1} \cup S_{2} ) $ = $\lim \mu (    B^{1}_{n}   \cup  B^{2}_{n}     )$ = $\lim \mu (    B^{1}_{n}) $  +   $\lim \mu (   B^{2}_{n}     )$ = $ \widetilde{\mu} (S_{1} )   $ + $ \widetilde{\mu} (S_{2} )  $ .

Therefore, $ \widetilde{\mu} $ is finitely additive.

\end{proof}

\begin{lemma}\label{L:9} $ \widetilde{\mathbf{S}}$ is a $\sigma$-algebra.
\end{lemma}

\begin{proof}
Let $S_{i} \in$ $ \widetilde{\mathbf{S}}$ be mutually disjoint and $\{B^{i}_{n}\} $ correspond to each $S_{i}$, for all i $ \geq$ 1. By lemma $\ref{L:6}$ and remark $\ref{R:2}$, we have $\sum_{i=1}^{n} \mu^{\ast}(S_{i}) = \sum_{i=1}^{n} \widetilde{\mu} (S_{i})= \widetilde{\mu} ( \cup_{i=1}^{n} S_{i})$= $\mu^{\ast}( \cup_{i=1}^{n}   S_{i} )   $.
We will show that $\cup_{i=1}^{\infty}   S_{i}$ $\in \widetilde{\mathbf{S}}$. First we will show that
\[
\mu^{\ast}( \cup_{i=1}^{\infty}   S_{i} ) \leq \sum_{i=1}^{\infty} \mu^{\ast}(S_{i})  <  \infty .
\]

For any $n$, $\mu^{\ast}( \cup_{i=1}^{\infty}   S_{i} ) \leq $ $\mu^{\ast}( \cup_{i=n+1}^{\infty}   S_{i} ) $ + $\mu^{\ast}( \cup_{i=1}^{n}   S_{i} ) \leq $ $\mu^{\ast}( X ) + \mu^{\ast}( X )$ by the subadditivity of $\mu^{\ast}$.
Thus, $\mu^{\ast}( \cup_{i=n+1}^{\infty}   S_{i} ) $ + $\sum_{i=1}^{n} \mu^{\ast}(S_{i}) \leq $ 2$\mu^{\ast}( X )$ = 2$\mu (X)$ for any n. By the finiteness of $\mu$ and the subadditivity of $\mu^{\ast}$, we must have $\mu^{\ast}( \cup_{i=1}^{\infty}   S_{i} )$ $\leq$  $\sum_{i=1}^{\infty} \mu^{\ast}(S_{i}) \leq$ 2$\mu( X ) <  \infty$ $\  $ (2).

Now we are going to construct a $\mu$-Cauchy sequence which converges to $\cup_{i=1}^{\infty}   S_{i}$ with respect to the pseudometric $d (\cdot,\cdot)$ = $\mu^{\ast} (\cdot \triangle \cdot)$.

\[\begin{array}{cccccc}
  B^{1}_{1} & B^{1}_{2} & \cdots & B^{1}_{k}  & \cdots & \longrightarrow S_{1} \\
  B^{1}_{1} \cup B^{2}_{1} & B^{1}_{2} \cup B^{2}_{2} & \cdots & B^{1}_{k} \cup B^{2}_{k} & \cdots & \longrightarrow S_{1} \cup S_{2} \\
  \vdots & \vdots & \vdots & \vdots & \vdots & \vdots   \\
  B^{1}_{1} \cup B^{2}_{1} \cdots \cup B^{m}_{1} & B^{1}_{2} \cup B^{2}_{2} \cdots \cup B^{m}_{2} & \cdots  & B^{1}_{k} \cup B^{2}_{k} \cdots \cup B^{m}_{k} & \cdots & \longrightarrow S_{1} \cup S_{2} \cup \cdots \cup S_{m} \\
  \vdots & \vdots & \vdots & \vdots & \vdots & \vdots
\end{array}\]

Note that for each $S_{1} \cup S_{2} \cup \cdots \cup S_{m}$, we can choose a $K$ so that $B^{1}_{K} \cup B^{2}_{K} \cdots B^{m}_{K}$ is arbitrary close to it in terms of the pseudometric $d (\cdot,\cdot)$.

Now, (2) implies for any $L$ there exists an $N_{L}$ such that $\mu^{\ast}( \cup_{i=N_{L}+1}^{\infty}   S_{i} ) $ $\leq  \sum_{i=N_{L}+1}^{\infty} \mu^{\ast}(S_{i})$  $< \frac{1}{2L}$. Moreover, for each $N_{L}$ there exists an $K_{L}$ such that

$ \mu^{\ast} ( S_{1} \cup S_{2} \cup \cdots \cup S_{N_{L}}    \    \triangle  \  B^{1}_{K_{L}} \cup B^{2}_{K_{L}} \cdots B^{N_{L}}_{K_{L}}   )  < \frac{1}{2L}  $.
Thus, by Lemma $\ref{L:2}$

\[
\mu^{\ast}(\cup_{i=1}^{\infty}   S_{i}  \triangle  \cup_{i=1}^{N_{L}} B^{i}_{K_{L}}     ) \leq  \mu^{\ast}(\cup_{i=N_{L}+1}^{\infty}   S_{i}) + \mu^{\ast}(\cup_{i=1}^{N_{L}}   S_{i}  \triangle  \cup_{i=1}^{N_{L}} B^{i}_{K_{L}}     ) < \frac{1}{L}.
\]

Now, call $Y_{L} $ =  $\cup_{i=1}^{N_{L}} B^{i}_{K_{L}}$ for each $L$. By design, $\{ Y_{L} \}$ converges to $\cup_{i=1}^{\infty}   S_{i} $. Also by the triangle inequality, $\mu ( Y_{n} \triangle Y_{m})$=$\mu^{\ast} (Y_{n} \triangle Y_{m}) \leq$ $\mu^{\ast} (Y_{n} \triangle \cup_{i=1}^{\infty}   S_{i}) + \mu^{\ast} (\cup_{i=1}^{\infty}   S_{i} \triangle Y_{m})  $ implies $\{ Y_{L} \}$ is a $\mu$-Cauchy sequence.

Thus, $\cup_{i=1}^{\infty}   S_{i} \in   \widetilde{\mathbf{S}} $. Therefore, $\widetilde{\mathbf{S}} $ is a $\sigma$-algebra.

\end{proof}

\begin{lemma}\label{L:7} $  \widetilde{\mu}$ is a countably additive measure on $ \widetilde{\mathbf{S}}$.

\end{lemma}

\begin{proof}
By (2) for any $\epsilon > 0$ there exists  an $M $ such that $\widetilde{\mu} ( \cup_{i=n+1}^{\infty}   S_{i} ) \leq$ $ \sum_{i=n+1}^{\infty}   \widetilde{\mu}   ( S_{i} ) < \epsilon $ for $n \geq M  $.

Moreover, $\widetilde{\mu} ( \cup_{i=1}^{\infty}   S_{i} ) = $ $  \widetilde{\mu} ( \cup_{i=n+1}^{\infty}   S_{i} ) + \widetilde{\mu} ( \cup_{i=1}^{n}   S_{i} )   = $ $   \widetilde{\mu} ( \cup_{i=n+1}^{\infty}   S_{i} ) + \sum_{i=1}^{n}   \widetilde{\mu}   ( S_{i} )   $ for all $n$ by Lemmas 6, 7, and 8.

Thus, $\widetilde{\mu} ( \cup_{i=1}^{\infty}   S_{i} )$ =  $\sum_{i=1}^{\infty}   \widetilde{\mu}   ( S_{i} )$. Therefore, $\widetilde{\mu}$ is a countably additive measure on $ \widetilde{\mathbf{S}}$.

\end{proof}

\begin{theorem}\label{T:1} ($\widetilde{\mu}$, $ \widetilde{\mathbf{S}}$) is a measure space.
\end{theorem}

\begin{proof}
The claim follows by Lemmas $\ref{L:9}$ and $\ref{L:7}$.
\end{proof}

\begin{theorem}\label{T:2}
$E$ is a measurable set iff  $E$ is in $ \widetilde{\mathbf{S}}$.
\end{theorem}

\begin{proof}
Suppose now $E$ is measurable. $\mu^{\ast}( E ) < \infty$ implies for any $n$ there exists an $C_{n}=  \cup_{i=1}^{\infty} A^{n}_{i}$ where $A^{n}_{i} \cap A^{n}_{j} = \emptyset $ for i $\neq$ j , $A^{n}_{i} \in \Omega$ for all i $\geq$ 1 such that $E$ $\subseteq $ $C_{n}$ and  $\mu^{\ast}( E )$ $>$ $\mu^{\ast}( C_{n} )$ - $\frac{1}{2n}  $. Now $E$ is measurable implies $\mu^{\ast}( C_{n} )$ = $\mu^{\ast}(C_{n} \cap E)$ +    $\mu^{\ast}( C_{n} \cap E^{\textbf{C}})$ = $\mu^{\ast}(C_{n} \triangle E)$ +  $\mu^{\ast}( E )$ which implies $\mu^{\ast}(C_{n} \triangle E)$ $<$ $\frac{1}{2n}$. Furthermore, $\mu^{\ast}( C_{n} )$ = $\sum_{i=1}^{\infty} \mu^{\ast}( A^{n}_{i}   )$ $<$ $\mu^{\ast}( E )$ + $\frac{1}{2n}$ implies there exists an $N_{n}$ such that  $\sum_{i=N_{n} + 1}^{\infty} \mu^{\ast}( A^{n}_{i}   )$ $<$  $\frac{1}{2n}$ $ \ $ (3). Let $ C_{n}^{N_{n}}  $ = $ \cup_{i=1}^{N_{n}} A^{n}_{i}  $. By the triangle inequality and (3), we have
$\mu^{\ast}(  C_{n}^{N_{n}}   \triangle E)$  $\leq$  $\mu^{\ast}(  C_{n}^{N_{n}}   \triangle  C_{n}  )$ + $\mu^{\ast}(  C_{n}  \triangle E)$ $\leq$ $\frac{1}{n}$. By design  $C_{n}^{N_{n}}$ is in $\Omega$. Moreover, by the triangle inequality for $n > m$, $\mu^{\ast}(  C_{n}^{N_{n}}   \triangle C_{m}^{N_{m}} )$  $\leq$  $\mu^{\ast}(  C_{n}^{N_{n}}   \triangle  E )$ + $\mu^{\ast}(  C_{m}^{N_{m}}    \triangle E)$ $\leq$ $\frac{2}{m}$ implies  $\{ C_{n}^{N_{n}} \} $ is a $\mu $-Cauchy sequence. Hence $E \in$  $ \widetilde{\mathbf{S}}$.\\

Suppose $E \in $ $ \widetilde{\mathbf{S}}$. Then there exists a $\mu$-Cauchy sequence $ \{ B_{n} \}$ such that
$ \lim \mu^{\ast} ( B_{n}   \triangle E)  =0   $. It follows we must have $ \lim \mu^{\ast} ( B_{n}   \cap E^{\textbf{C}} )  =0   $ and $ \lim \mu^{\ast} ( (B_{n}) ^{\textbf{C}}   \cap E)  =0   $ $ \ $ (4). Note for $A \in$ $ \mathbf{P}(X)$ we must have

$\mu^{\ast}( A ) \leq $ $\mu^{\ast}( A \cap E ) $ + $\mu^{\ast}( A \cap E^{\textbf{C}} ) $ by the subadditivity of $\mu^{\ast}$. Moreover, $B_{n}$ is measurable for each $n$ implies $\mu^{\ast}( A )$ = $\mu^{\ast}( A \cap B_{n} ) $ + $\mu^{\ast}( A \cap (B_{n})^{\textbf{C}} ) $, $\mu^{\ast}( A \cap E)$ = $\mu^{\ast}( A \cap E \cap B_{n} ) $ + $\mu^{\ast}( A \cap E \cap (B_{n})^{\textbf{C}} ) $ and $\mu^{\ast}( A \cap E^{\textbf{C}})$ = $\mu^{\ast}( A \cap E^{\textbf{C}} \cap B_{n} ) $ + $\mu^{\ast}( A \cap E^{\textbf{C}} \cap (B_{n})^{\textbf{C}} ) $ $ \ $ (5).

Now by taking limits on both sides of (5) and using (4),

we get $\mu^{\ast}( A )$ = $ \lim \mu^{\ast}( A \cap B_{n} ) $ + $ \lim \mu^{\ast}( A \cap (B_{n})^{\textbf{C}} ) $, $\mu^{\ast}( A \cap E)$ = $\lim \mu^{\ast}( A \cap E \cap B_{n} ) $, and $\mu^{\ast}( A \cap E^{\textbf{C}})$ = $ \lim \mu^{\ast}( A \cap E^{\textbf{C}} \cap (B_{n})^{\textbf{C}} ) $. Moreover, $A \cap E \cap B_{n}$ $\subseteq $ $A \cap B_{n}$ and $A \cap E^{\textbf{C}} \cap (B_{n})^{\textbf{C}}$  $\subseteq $ $A \cap (B_{n})^{\textbf{C}}$ implies

$ \lim \mu^{\ast}( A \cap B_{n} ) $ $\geq$ $\mu^{\ast}( A \cap E)$ and  $ \lim \mu^{\ast}( A \cap (B_{n})^{\textbf{C}} ) $ $\geq$ $\mu^{\ast}( A \cap E^{\textbf{C}})$. Thus, we must have $\mu^{\ast}( A )$ $\geq$ $\mu^{\ast}( A \cap E)$ +    $\mu^{\ast}( A \cap E^{\textbf{C}})$. Hence, $\mu^{\ast}( A )$ = $\mu^{\ast}( A \cap E)$ +    $\mu^{\ast}( A \cap E^{\textbf{C}})$ and $E$ is measurable.

\end{proof}

\section{Conclusion}
 Theorems $\ref{T:1}$ and $\ref{T:2}$ show that the measure space ($\widetilde{\mu}$, $ \widetilde{\mathbf{S}}$) agrees with the Caratheodory Extension when $\mu$ is a finite measure. Moreover, theorem $\ref{T:2}$ show that measurable sets are exactly limit points of $\mu$-Cauchy sequences. The $\sigma$-finite case follows from the finite case.

     .
\section{Acknowledgement}
 The first author would like to thank his grandfather Waichi Tanaka for his inspiration and financial assistance and Andrew Aames for encouraging him to progress through the graduate program. With the kind support of both, the first author has progressed further than he ever thought possible. In addition, both authors would like to thank professor Michel L. Lapidus, and professor James D. Stafney for their professional advice on this paper, and to Anne Hansen for her editing assistance.

redpajama_set_name: RedPajamaArXiv


Forward Chris Wilcox said he is ready to play tonight against the Los Angeles Clippers, five days before the earliest possible return date the team gave in its initial 10-14 day recovery timetable from a dislocated left ring finger.
"I'm just going to play my game. I can't worry about it," said Wilcox, who will wear a soft cast on his middle two fingers when he returns. "If it gets hurt again it gets hurt again. But I just have to keep being physical."
Thunder coach Scott Brooks would not say whether Wilcox will be active tonight but said he looked good during the team's light practice Monday.
"He's still a little conservative with it, but you have to fight through the pain that you have," Brooks said. "But he did show signs of improvement."
Rookie guard Russell Westbrook scored a season-low two points on 1-for-3 shooting in Sunday's loss to San Antonio, getting in early foul trouble and playing just 19 minutes.
"All players are going to have some rough spots, and that was a rough spot for him," Brooks said. "We will look at film and try to get better together with him. But it's just part of going through the ups and downs of an NBA player, whether he's a young player or a veteran player. They're going to have games that they wish would have never happened."
Westbrook is averaging 14.4 points in five games following a contest in which he failed to score in double digits.
"We would love to have a great home game. Our fans deserve it. Our players deserve it." - Brooks on the beginning of a three-game home stretch.
Robert Swift is participating in full contact games of one-on-one but has yet to return to practice. Assistant coach Mark Bryant delivered a shot to Swift's healing back following Monday's practice, indicating Swift has healed. Swift could return to practice Wednesday or Thursday but is still listed as day-to-day. ...Desmond Mason, Damien Wilkins and Joe Smith delivered shoes to more than 150 students at Dunbar Elementary School on Monday afternoon.


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Herbert W Armstrong
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The Holy Land - Yesterday, Today and Tomorrow
Ernest L Martin Church of God
Died: January 16, 2002
Ambassador College: 1958
Ordained: January 2, 1959
Office: Elder
The Holy Land of Jesus' time was totally unlike what people imagine it to have been. And it was far from being a back — ward country full of itinerant shepherds and oriental casbahs. It was a land of wealth and beauty — one of the greatest exponents of Greek culture in the ancient world. Yet all of its present and former glory fades into obscurity in the light of the prophesied preeminence the Holy Land is to have in God's Kingdom — soon to come!
TODAY the land of Israel is often described as a land of contrasts. Major cities rise on what were formerly just sand dunes. Where there was once desert or swamp, one sees thriving farms today. But why the desert and swamp to begin with? Was this not the "land of milk and honey"?
Today one is still staggered by the denuded slopes of the central mountain chain — they are treeless and so dry. Has it always been this way? What had happened to this land which was once the envy of the world? What was it like in the time of Christ?
Most of us have associated this ancient area with camels, donkeys and people dressed in Bedouin garb. But this is nothing like it formerly was. Eyewitness reports give us an astonishingly different description.
The most important witness was Josephus, the Jewish historian who lived in the first century. Williamson — who has given us one of the finest translations of Josephus — graphically sums up his overall description. He notes how Josephus brings "before our eyes the cities, palaces, and temples which filled this little land with beauty and made it one of the greatest creations of Hellenism, as different as could be imagined from the Palestine of our Sunday School memories... a country filled with such a wealth of architectural and artistic splendor as has perhaps never been elsewhere since the world began, and (subsequently) reduced by crimes and follies to a desert, a mass of shapeless ruins" (Introduction, Penguin Ed.).
These two statements of Josephus' translator begin to tell us how the Holy Land really was. It was nothing like it is today!
Herod the Great — Builder Extraordinary
The building up of this area, making it one of the most prosperous areas in the world, was started two centuries before Christ. But the greatest activity came in the time of Herod the Great. We need to recognize the cultural advances implemented by Herod and his successors. They made this country into a showplace of Greek culture and Hellenistic splendor which turned it into a prime example of classical grandeur in the first century.
Herod's accomplishments occurred just before the birth of Christ. The darker side of his life has been adequately penned by Josephus and the Gospel writers. Yet there was a trait in Herod's character which may, in one way, allow the historian to give him his common title, "the Great." The reason? He was one of the most prodigious builders of all time. His structures were never ordinary in size or common in esthetic values. No one could match Herod in his lavish outlays of resources for the building of whole cities, temples, harbors, theaters, amphitheaters, hippodromes, palaces, as well as parks, gardens, roads, etc. Not only did his building enterprises extend through his own territory, but his generosity spread throughout the Eastern Roman Empire. What he created in the three decades of his rule was such a prosperous kingdom that "its external splendor recalled the traditional magnificence of Solomon" (McClintock and Strong, Cyclopaedia of Biblical, Theological and Ecclesiastical Literature, Vol. IV, art. "Herod").
What a comparison! Herod's kingdom became much like Solomon's in its riches. But where did his wealth come from? Could the land of Herod and his surrounding domains support such extravagant building expenditures? The answer is most decidedly YES! This land was different in those days. The whole area was very prosperous.
Josephus Describes Galilee, Samaria, Judaea
Speaking of the land in general, Josephus relates that the fruitfulness of the land made it like "a garden of God in which there grow the most precious and most beautiful trees in amazing variety."
Of Galilee in particular — the northern region of the Holy Land where Christ had His home and where He conducted most of His ministry —Josephus states:
The whole area is excellent for crops or cattle and rich in forests of every kind, so that by its adaptability it invites even those least inclined to work on the land. Consequently every inch has been cultivated by the inhabitants and not a corner goes to waste. It is thickly studded with towns, and thanks to the natural abundance the innumerable villages are so densely populated that the smallest has more than 15,000 inhabitants (Josephus, Wars of the Jews, III, 3, 2).
What about Judaea and Samaria in the southern and central regions? The hillsides were not like the barren, treeless, arid landscapes that we see in many parts today. Josephus tells us that both Judaea and Samaria
...are made up of hills and plains, with soil easily worked and repaying cultivation. They are well wooded and prolific in fruit, both wild and cultivated; for nowhere is the soil arid by nature and rain is generally ample. All their streams are remarkably sweet, and lush grass is so plentiful that the milk-yield of their cows is exceptionally heavy. The final proof of their outstanding productivity is the swarming populations of Judaea and Samaria (ibid., para. 4).
Ambassador College Photo — A view of the Sea of Galilee from its surrounding hills — green and productive as in the days of Josephus.
Where did Herod get his abundance of wealth which became proverbial throughout the Roman world? It came from the land and from the productive people that lived on it. In the time of Christ, it was one of the wealthiest areas in the whole Roman Empire! All people of the time knew it. Josephus admitted that "of all the cities under Roman rule, our own (Jerusalem) reached the highest summit of prosperity" (Wars of the Jews, Preface, 4).
It can easily be demonstrated why it became so prosperous. Other areas of the Roman Empire (other than certain regions of Asia Minor, Syria and Egypt) were no match for wealth. Vast tracts in Italy — the very heartland of the Empire — were veritable wastelands created by the Hannibalic, Social and Civil Wars. Greece was in shambles — not even a facade of its former self.
Spain and Gaul were undeveloped. It was the East that carried the financial burden of the Empire, and proportionately it was the Herodian region that led most others. Even Titus, the later Roman Emperor, stated that the land of Herod "had become richer than Rome itself" (Josephus, Wars of the Jews, VII, 1, 2).
The Building Projects of Herod
Herod was a great Hellenist — a great exponent of classical Greek culture. His buildings had the stamp of classical Greece all over them. The cities he built were not like the typical ones found in the Middle East today. They were thoroughly "Greek" with many special embellishments created by Herod himself. The guiding principle which motivated Herod and his architects was to make things bigger and better than any other in existence. Splendor was the keynote.
One of his monumental buildings, which the people of the Roman world admitted to be the most impressive structure on earth, was the Temple which Herod rebuilt on Mount Moriah in Jerusalem. With all its magnificence, scope, grandeur — gold, rare woods, lavish marble decorations and colossal walls — no building of the twentieth century could begin to compare with it. Herod built the Temple to be one of his crowning achievements — and so it was. It took over 70 years to complete. But strangely, it was finished about 6 years before it was destroyed by the Romans. All that remains today is some of its platform on which the outer courts of the Temple stood, and part of its walls (the famous western — or "Wailing" Wall).
The Temple was an immense structure. It was built on a gigantic stone platform with walls on all sides. These surrounding walls were about a mile in length, 200 feet high and in some places 18 feet thick. Josephus said that "the wall was itself the most prodigious work that was ever heard of by man" (Antiquities of the Jews, XV, 11, 3). Surrounding the Temple enclosure and abutting to the inside of its massive walls was a covered arcade or walkway 45 feet wide and supported by Corinthian columns. Each of the columns — about a thousand in number — was made of single stones, circular in shape, with Corinthian capitals decorated in gold. The ceiling of this arcade was paneled with cedar. "The natural magnificence of it all, the perfect polish, the accurate jointing," said Josephus, "afforded a remarkable spectacle."
But beside the colossal walls and arcade, there was the sanctuary itself near the center of the platform. The sanctuary was made of the finest marble and was the height of a ten-story building. All its gates were covered with gold and its many decorations were of the best workmanship imaginable.
The Sanctuary had everything that could amaze either mind or eyes. Overlaid all around with stout plates of gold, in the first rays of the sun it reflected so fierce a blaze of fire that those who endeavored to look at it were forced to turn away as if they had looked straight at the sun. To strangers as they approached it seemed in the distance like a mountain covered with snow; for any part not covered with gold was dazzling white (Wars, V, 5, 6).
The present archaeological excavation at the southwestern angle of the ancient Temple walls — an excavation sponsored jointly by Hebrew University and Ambassador College (see pictures on page 44) — is uncovering some of the relics associated with this fabulous structure. The archaeologists on the "dig" keep remarking about the sheer majesty and glory of these remains. Herod did nothing in a small way. As an example, the "dig" has been excavating the foundations of piers that supported the largest bridge ever constructed in the Roman Empire — a bridge so enormous that a modern superhighway could be placed on top quite easily. There was certainly nothing common about Herod's building enterprises.
An example of this is another building which almost took the breath away to view it. This was the palace which Herod built for himself in Jerusalem. It was so splendid that Josephus said no tongue could possibly describe it. Leaving aside Herod's own beautiful quarters, this magnificent palace contained immense banqueting halls and quite a number of guestrooms, each having spaces for 100 beds. All the stones of the floors were of different colors — stones that everywhere else were looked on as rare were found in Herod's palace in great profusion. No two of the many rooms were designed alike, and they were all luxuriously furnished mostly with gold and silver. And adjacent to the many rooms were open spaces of green lawns surrounded by columned arcades. There were all kinds of trees along the walkways and these were flanked by watercourses and pools adorned with bronze statues through which water poured out. Josephus said this palace was so wonderful that it almost made the Temple itself seem insignificant.
But there were many marvelous structures that made Jerusalem one of the most beautiful cities on earth — buildings which put ancient Athens, Rome and Alexandria in the shade. Right next to the Temple, Herod built one of the largest citadels in the East. It was described as being more like a sumptuous castle or palace than a fortress. Then there was the amphitheater, which looked much like the later coliseum built in Rome. To this amphitheater were brought many wild animals, great quantities of lions, and other beasts which were rarely seen in the Roman Empire. These beasts fought either one another or men in gladiatorial fights. Herod also built in Jerusalem a Greek theater as well as a hippodrome (where chariot and horse races, gymnastics and athletic events were held in imitation of the Olympic Games). Besides all this and numerous other buildings of elegance, there were public parks, many fountains, pools and extensive gardens found throughout Jerusalem.
On the cultural side, Herod surrounded himself with a circle of men accomplished in Greek literature and art. The highest offices of state were entrusted to Greek rhetoricians. Scholars and professional men came from all over the Empire to take advantage of Herod's generosity in the liberal arts and natural sciences. Herod was so infatuated by the Greek way of life that he even boasted of being more nearly related to the Greeks than to the Jews.
Ambassador College Photo — These rare gold coins were found in the later Arabic strata of the dig. (The vast majority of the coins found are small copper ones.)
In short, there was hardly a Hellenistic city anywhere in the world that could compare in grandeur to the city of Jerusalem in the time of Jesus.
Herod's Other Achievements
The Holy Land was dotted with cities and towns based on Greek architectural designs. Herod beautified a new Jericho — constructing in the city a palace and a fortress. He also gave the inhabitants a theater, amphitheater and hippodrome, plus a good number of public buildings. At Paneum, near the source of the Jordan River (the Caesarea Philippi of the New Testament), he constructed a great temple to Caesar of the finest stones available. Then about 10 miles south of Jerusalem he raised up an artificial mountain more than 300 feet high and on top constructed a fortress so magnificent that it is described as being more of a palace than a citadel. He also fortified lavishly the famous Masada, and sites east of Jordan.
But even these things did not contain Herod's ambitions for building. Selecting a spot on the Mediterranean Sea where there was a small town in the state of decay, he decided to build — with tremendous natural odds against him — a brand new city and harbor. Spending a vast amount of money, he first lowered into the water gigantic rectangular stones to form a breakwater. Most of the stones were 50 feet long, 9 feet deep and 10 feet broad. Beginning from the shore he continued this breakwater out into the Mediterranean in a circular fashion until some of the stones were being lowered into 120 feet of water. After bringing this breakwater to the surface, he then built a mole on top which was 200 feet wide. On this were erected many buildings for seamen and fishermen. Opposite this artificial harbor which he had now created, he built a temple to Caesar with a statue of the emperor so large (it was over 40 feet high) that it matched the Olympian Zeus — one of the Seven Wonders of the World. The rest of the buildings and statues of this new city were of the largest scale — many other works in the Roman Empire being dwarfed by comparison. Because this new city was one of the greatest creations of the time, Herod named it after Caesar, calling it Caesarea. The city is mentioned in Acts 10:1.
This, however, was not all. The old city of Samaria in the hill country of Ephraim was completely reconstructed on a scale almost equaling Caesarea. Herod also built two complete cities near Jericho. Then he rebuilt the coastal city of Anthedon, which had been destroyed in war, with his customary grandeur. And we must not forget the great commercial city of Antipatris which he raised up in the Plains of Sharon.
Herod's close friendship with Caesar Augustus, the Roman emperor, gave him many natural advantages needed to undertake these magnificent building projects. And to show his thankfulness to Caesar, Josephus says,
I cannot think of any suitable spot in his kingdom that he left without some tribute of esteem for Caesar. When he had filled his own country with temples, these tributes overflowed into his provinces, and in city after city he erected a Caesareum (a temple to Caesar) (Wars, I, 21, 1-8).
But there was more. Not only were Herod's provinces so rich that he made his kingdom the showplace of the world, he also showered his generosity on many far-flung cities and areas.
For Tripolis, Damascus, and Ptolemais he provided gymnasia, for Byblus a wall, for Beirut and Tyre, halls, colonnades, temples, and marketplaces, for Sidon and Damascus theaters, for the coastal Laodicea an aqueduct, for Ascalon baths, magnificent fountains, and cloistered quadrangles remarkable for both scale and craftsmanship; in other places he dedicated woods and parks.... Corn he bestowed on all who needed it. To Rhodes he over and over again gave money for naval construction, and when the temple of Apollo was burnt down he rebuilt it with new splendor out of his own purse. What need be said of his gifts to Lycia or Samos, or of his liberality to the whole of Ionia [this means the cities of Ephesus, Smyrna, Troas, etc.), sufficient for the needs of each locality? Even Athens and Sparta, Nicopolis and Mysian Pergamus are full of Herod's offerings, are they not? (ibid., para. 11)
And then, as though this were not enough, he was able to help one of the greatest cities of the East — Antioch. That city did not have enough money to pave even its principal street. But what did Herod do? He paved 2¼ miles of it with the finest polished stone available. And to secure his fame in that city he built an arcade over the street supported by sumptuous Corinthian columns from end to end. This was to keep the rain off the people using this creation of Herod's.
And when the Olympic Games in Greece were in danger of ceasing because of a lack of funds, Herod donated such a gift of money for their upkeep that the committee made him president of the Games. And to perpetuate the memory of this honor, he "endowed them for all time with an income big enough to ensure that this presidency would never be forgotten" (ibid.).
To sum up, Josephus says:
As for his other benefits [to various nations], it is impossible to reckon them up, those which he bestowed on cities, both in Syria and Greece, and in all the places he came to in his voyages (Antiquities, XVI, 5, 3).
There can be no doubt, Herod's kingdom was one of the richest in the Roman Empire. As Josephus said, the Holy Land had reached "the summit of prosperity."
The Roman-Jewish War Ended It All
This land in the time of Christ was the jewel of the East. Its buildings were so beautiful, its fortresses so strong, its financial capacity so great, that no one would have imagined that all of it would be reduced to ashes and complete ruin within a generation.
But there was someone who knew. That person was Jesus Christ!
Not long before His crucifixion, Jesus climbed to the summit of the Mount of Olives overlooking Jerusalem on the east. When His disciples called attention to the grandeur of the Temple and the city, He answered, "Seest thou these great buildings? There shall not be left one stone upon another that shall not be thrown down" (Mark 13:2).
Who could have believed such a prophecy? The most prosperous area in the Empire being reduced to oblivion? This seemed absurd and beyond belief! But this is what Christ prophesied, and within a generation it had come true — so true. Christ had said that "when ye shall see Jerusalem compassed with armies, then know that the DESOLATION thereof is nigh" (Luke 21:20).
Ambassador College Photos left, above: courtesy of Hebrew University — Opposite are some views of the Mount of Olives: (top] an olive tree on the Mount, and (bottom) looking at it from across the Kidron Valley on the Temple Mount. In Herod's time the hillside was covered with gardens and olive trees. Above are shots of typical ruins found in the many archaeological excavations in Israel.
When the Jews revolted against the Romans, the Roman armies surrounded the city, but then, for some unknown reason, suddenly retreated. This gave the followers of Christ a chance to heed His command to flee the city. But who could have believed that Jerusalem's desolation was nigh at hand, except those who trusted in the prophecy of Christ? Within months it was all over — the once beautiful Jerusalem and Judaea, the pride of the world, lay in utter desolation. Listen to Josephus' melancholy description of Judaea and Jerusalem after the war was over:
The countryside like the City was a pitiful sight; for where once there had been a lovely vista of woods and parks there was now nothing but DESERT and the stumps of trees. No one — not even a foreigner —who had seen the old Judaea and the glorious suburbs of the City, and now set his eyes on her present desolation, could have helped sighing and groaning at so terrible a change; for every trace of beauty had been blotted out by the war, and nobody who had known it in the past and came upon it suddenly would have recognized the place (Wars, VI, 1, 1).
The Romans took away to various parts of the Empire much of the remaining people and also carted away many of the beautiful stones and other fineries that made up this once-glorious land. It has been said that if the ruins of these Herodian cities, buildings and temples had been left rather than taken away, classical admirers would not be going to Greece or Western Asia Minor to see the remains of the Hellenistic world. They would be coming to Jerusalem and the surrounding area. But almost all of it was taken away over the decades that followed the disastrous Roman-Jewish War. And of the Temple building itself, not one stone remains upon another. With that war, the external splendor of the Holy Land — a glory that approached that of Solomon's, completely disappeared. The Roman-Jewish War began its decline. The wars that came in its wake, over the centuries, have further reduced it to the state that it is in now. But has his glorious land of Christ's time with is beauty and prosperity been banished forever?
Restoration Prophesied
The time is soon coming when the Holy Land will regain its prosperity — and even on a grander scale than the times of Solomon and Herod put together! The prophet Joel said that the Lord will "be jealous for his land, and pity his people.... I will send you corn, and wine, and oil, and ye shall be satisfied therewith... for the pastures of the wilderness do spring, for the tree beareth her fruit, the fig tree and the vine do yield their strength... the floors shall be full of wheat, and the vats shall overflow with wine and oil... ye shall eat in plenty, and be satisfied, and praise the name of the Lord your God, that hath dealt wondrously with you.... And it shall come to pass in that day, that the mountains shall drop down new wine, and the hills shall Flow with milk, and all the rivers of Judah shall flow with waters" (Joel 2:18, 19, 22, 24, 26; 3:18).
A start in this direction is already being made. Reforestation has started in many areas. Cities are becoming more modern and areas are being cleaned up and beautified. Even the Hebrew University and Ambassador College archaeological dig is helping to clear the debris that has covered Zion for the past nineteen hundred years. God has started the rejuvenation already. Yet the complete fulfillment of Joel's prophecy will come when Gods' true Messiah, Jesus Christ, returns to this earth. This is when the area will return to its pristine glory — becoming again a land of milk and honey, the true Promised Land of God. It will then become the center of the earth — politically, culturally, economically and spiritually. The glory of the Holy Land will return, but on a much grander scale. God speed that day.
Tomorrow's World Magazine November-December 1970 Vol II, No. 11-12
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mmmmm . . . Mac and Cheese!
You are here: Home / Wendy Knits / mmmmm . . . Mac and Cheese!
Furthering my love for all things orange, I made mac and cheese this weekend. Here's what I did.
Cook the elbow macaroni according to package directions until al dente and drain. Set aside.
In a heavy saucepan, melt the butter over high heat. When just melted, dump in the flour and blend well with a wire whisk to make a roux. Cook for a minute or two over high heat, then reduce the heat to medium and slowly whisk in the milk. Add the spices and cook, whisking constantly, over medium heat until the sauce thickens.
Reduce the heat to low and stir in all but 1/4 cup of the cheddar cheese. Stir until the cheese is melted.
Add the cooked macaroni to the cheese sauce and mix until thoroughly incorporated.
Pour the mixture into a greased 3-quart casserole dish. Top with the reserved cheddar cheese and the parmesan cheese.
Bake in a 375-degree oven for about half an hour.
There are many variations you can employ in the making of the mac and cheese, but this is my favorite. The cayenne pepper and dry mustard add a nice little "bite" to it. Zesty!
Speaking of orange, I am on the edging of my shawl. Excitement abounds!
Lucy is the personification of excitement!
Yum! I love 'real' mac and cheese. My recipe is similar except instead of cayenne and mustard, I use cayenne and a touch of nutmeg (it's a James Beard recipe). As soon as it cools off around here I'm going to have to make some!
I love to do homemade mac n' cheese, but I use (horrors!) canned cream of mushroom soup instead of making a white sauce. I used to use hand-grated cheese but now I buy it already shredded, if I can find it sharp enough!
Now I need to learn how to make it for two instead of 12. That's the hard part!
Lucy is so excited she's fainted!
Marion, I think Lucy's just full of mac and cheese and is having a nap. Might be excitement though.
Shawl is beautiful. Colorway is very interesting in the way that it lightens very much as sky does when sun rises. Thanks for sharing.
do you believe that just a half hour ago I was takin' stock of the over abundance of cheese in my fridge and thinkin' about mac and cheese! I might just try this version later. of course, that means I'll have to go to the store for milk. ::sigh:: Maybe tomorrow.
mias last blog post..Good thing I took my pillow.
Hmmm…the color of the shawl looks suspiciously like the mac 'n' cheese. Is it the fate of bad shawls to be baked at 375 for 30 minutes?
mmm, homemade mac and cheese is the best!
Thank you so much for this mac& cheese recipe with the extra kick. I think it suits your personality – wholesome with just enough spice to make it interesting.
I'll think I'll have to make some when it isn't ninety degrees.
That sounds really yummy! Thanks for sharing!
I'm looking at the similarity between the finished mac 'n cheese (yum! Do want!) and the shawl… I think we're going to henceforth have to call the pattern and color combination the Mac 'n Cheese Shawl.
Ohhhhh Myyyyyy that mac n' cheese looks yummy! I am definitely going to try the recipe out.
The shawl is lookin' great too… almost done!
Yummy! (both the shawl AND mac/cheese). Fall is in the air in Central PA and Mac and Cheese (especially your recipe) is a good idea for dinner on a chilly evening. Your shawl, as always, is gorgeous!
I must keep my husband from your blog or he will insist I make him some Mac and Cheese and be a good wife.
Thank you so much for the Mac & Cheese recipe! I am always on the lookout for variations of my favorite comfort food! Nancy, I'm sorry to say that my son prefers the box kind,too – must be the lack of refined taste buds at that age!
The shawl is gorgeous! I love the way the colors deepen and brighten – it too reminds me of a beautiful sunset. Thank you for sharing it and the recipe!
How funny, I made homemade mac & cheese yesterday as well! It's one of the best comfort foods I've ever found.
How funny! I made homemade mac 'n' cheese on Friday. Fall is in the air. I put nutmeg in mine, but now that I read Rachel's comment, I may have to also add cayenne! My kids would love that.
Mac 'n' cheese, mmmmm. I even love Kraft's.
What a yummy meal! BTW, I love your blog so much that I have a little something for you over on mine.
I hate to nag, Wendy, but weren't you supposed to "take it easy" with the knitting? You're on the edging and you just started a few days ago. I know you knit a lot faster than I (or most mortals) but I don't want you to exacerbate your condition. End of caring lecture.
That's some fast knitting on that shawl!
And you had time to cook too 😉 Sounds like a tasty mac n cheese.
Thanks for the recipe. Sounds and looks yummy! Love the color of the shawl, btw!
That sounds like a great receipe will have to try it. Would you believe we had mac and cheese last night for dinner. Fall is in the air, and that is my favorite comfort food. Shawl is beautiful. Thanks for sharing receipe.
Must be in the air. My daughter requested the boxed kind for lunch today! She also likes the baked mac n cheese and will request a bowl once the sauce is made pre-baking.
Love your mac n cheese shawl because that is what it looks like in its unblocked state.
YUM!! Must make some tomorrow.
Beautiful shawl and I can tell Lucy loves it by her excited posture.
I have saved your recipe, even though the only difference from mine is the cayenne pepper and dry mustard. It just sounds so good!
Thatlooks absolutely yummy!! I am going to try that tomorrow!! Thanks for the recepe!! Lucy is wonderful as usual!! Have a pieceful Monday!!!
So did the shawl inspire the mac & cheese? in the pics, they look very similar in color…lol. I love a good homemade mac & cheese. Might have to add that to the menu this week!
The shawl look gorgeous. I dearly wish I could knit that fast!
The recipe looks good, thanks for sharing. Did Lucy get any cheddar cheese while you were cooking? Our kitty prefers Swiss.
I think I'll try this recipe out tomorrow! We seem to have switched into Fall mode pretty quickly here in the Northwest and mac-n-cheese would hit the spot. A couple years ago my Mom made homemade mac-n-cheese for my niece & nephew who….didn't really like it. They wanted "real" macaroni – the kind that comes out of the blue & yellow box. 🙁 They also seem to think that frosting that comes out of a can is an actual food substance too. Yuuuuuuuk!
Mmmm, mac 'n cheese. That's exactly the way my mom used to make it for us, even down to the dry mustard and cayenne pepper. Yummy! Oh, and I like the shawl, too!
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Thank you for posting your recipe! There is nothing better than comfort food, although the Drs and dieticians may disagree. ahhh, this will be on the table this week!
Amazing that the orange colors are so similar. And both are yummy! This is so not far.
There's nothing like home made mac & cheese.
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Ummm…YUM! I'll have to whip that up on the first rainy dall of the fall…ultimate comfort food!
I gave your blog an award (which is probably 9 million and one now for you). Details are in my blog.


During the hot, lazy days of summer everyone likes to play in the water.
Swimming is a great activity, but did you know that drowning is the number two cause of childhood injuries nationwide in children 14 and under? In 2003, nearly 4,200 of these children were treated in hospital emergency rooms for accidental drowning-related incidents.
According to a recent study, nearly nine in 10 drowning-related deaths occurred while a child was being supervised. Children can drown in as little as one inch of water, so they are at risk in bathtubs, toilets, pools, spas - and even buckets with water or cleaning solution.
Erect fencing on all sides of the pool or hot tub. The fence should be at least 5 feet tall with self-closing and self-latching gates.
Find out when and where diving is allowed. Never dive in water less than nine feet deep.


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Canadian Centre for the Great War
History Worth Remembering	Island Report	Journalism
On the 4th of November, the Galerie Gora hosted an unusual art display of a dozen Belle Époque posters from the First World War. These propaganda posters were designed by celebrated French artists such as painter cartoonist Abel Faivre and painter illustrator Auguste Leroux. The event, a fundraiser for The Canadian Centre for the Great War, included a silent auction in which two of the original posters, donated by Centre founder, Mark Cahill, were auctioned off.
"The posters we will be showing at this event have never been displayed publicly," says Great War Centre curator Caitlin Bailey. "This will be the first time that these works will be hung so that people can see them properly."
Curator Caitlin Bailey examines Edwin Stewart Turner's uniform. Turner fought at the Battle of Courcelette with the 42nd Battalion.
Normally, over 85% of the 45 posters in the collection lie in storage on the second floor of an office in an old factory building on St. Patrick Street where the Canadian Centre for the Great War is housed.
These posters are part of the small museum's collection of between 3,000 to 5,000 artifacts which includes hundreds of personal letters, medals, uniforms, diaries, and wooden plaques from the war that ended 98 years ago this month – artifacts sprawled in the entrance and in a circuit of five rooms upstairs in Suite 202. Touring through the Centre with curator Caitlin Bailey is a treat for anyone who wants to hear personal stories about World War I soldiers and their families.
Read more at The Montrealer November 2016 Issue.
Honouring Fred Christie
Johanne Gervais Helps us Research our Ancestors
Getting Quotes from Attestation Papers


The most dangerous are bigger towns and cities, where people live close to one another.
The safety situation in Slovakia has slightly improved. The number of crimes dropped by nearly 3,000 in the third quarter of 2016 compared with the previous year. The total number is still high, however, amounting to nearly 54,000, the Sme daily reported.
The police has recently published new crime maps, depicting all types of crimes. They claim the number of thefts and other property crimes, as well as economic crimes, has dropped. On the other hand, there are more cases of moral and violent crimes.
The most dangerous places are bigger towns and cities where many people live close to one another without knowing each other and where many tourists come. This concerns especially the second Bratislava district, Košice, and Trnava, as well as Hlohovec and Piešťany, Sme wrote.