initializing module on django+mod_wsgi+apache
You are possibly just getting confused and are actually using as poor Apache/mod_wsgi configuration. Specifically, you are likely using embedded mode with Apache prefork MPM. That is bad because Apache will use lots of single thread processes and so the code has to be loaded in all of them. That is why you probably think it is happening on each request against the same process, where in reality, each request is hitting a different process.
Ensure you are using daemon mode of mod_wsgi and that your code is thread safe and so use single multithreaded process and it shouldn't have the issue.
Edit your question and add your Apache/mod_wsgi configuration snippets from Apache configuration file and state what Apache MPM you are using.
My django application is running on apache+wsgi. One of the module in my django app needs to load a Java library via jpype and this Java library takes long time to initialize due to its application nature. 
The problem is that, for each http request handled by django in apache+wsgi setup, this Java library is re-loaded. However, this does not happen when I run my same app in development web server (python manager.py runserver 8000). In development web server, it only loads the Java library only once. 
Is there any way to change apache or mod_wsgi configuration or my django app so that it won't reload my Java library for every http request?
Many thanks. 
Andy