.live, .delegate, and .do (JQuery >= 1.7 only) are the exceptions to the general rule of not using $(document) in JQM. These register to have your function called for all future events on the selector. You almost always want to do this on $(document).
I would recommend using .delegate currently, since .live will be deprecated in JQuery 1.7, and .do doesn't yet exist in 1.6.4 which you need to use if you are using JQM 1.0.1.
So, from my own code an example:
$(document).delegate("div.nearby-places-page", "pageinit", function(event) {
<code here>
});
This will run the code whenever the page with class nearby-places-page is initialized. The page will be initialized whenever it is loaded into the DOM - i.e. $(document). If, for example, you were to use the data-dom-cache="true" option on the page, then this event would occur exactly once.
You wouldn't want to use $.mobile.activePage as a qualifier in the selector because that wouldn't make sense. It would never be fired.
If you meant to have something happen every time the page is SHOWN, (which may or may not involve loading the page into the DOM - it may already be there) then you probably want to use a pageshow event.