JQuery / Javascript function requies both $(document).ready and $(document).ajaxSucces

JQuery / Javascript function requies both $(document).ready and
$(document).ajaxSucces

I have a JQuery / Javascript function that is to be used across my site
for some basic UI functionality. However, many of the elements that this
function effects, will be injected via Ajax, while others will be static
html.
Currenty I've been able to make my scripts work for me by duplicating the
function and applying both $(document).ready and $(document).ajaxSucces.
My question is: What is the appropriate accomplishing this?
Thanks, Mark