That's not what they are saying
Its a dumb example.
The servlet container (tomcat, jboss, whatever) constructs exactly one instance for each deployed servlet class and uses it to handle every single request.
This is a really annoying design choice as there is no nice way to have data that is page scoped without passing it around in all the calls. Hence my comment that ivars and static vars have roughly the same scope/lifetime in a servlet.
When they say persistence - they mean that the servlet instance stays around until the servlet is reloaded (container is bounced or source code is changed). So the values in the ivars are "persistent" from page request to page request.
What are you trying to do?
