Let be a measureable space (in fact Polish, so we can guarantee the existence of regular conditional probabilities), two probability measures on and two sub -algebras.
Let and be the regular conditional probabilities of and given .
If on and -almost everywhere
(i think it should say -almost everywhere too, but maybe it is implicit)
Any help regarding this step? What would be a proper approach?
I have tried to use the next properties:
-Conditional expectation (with respect to )
Just in case means the radon-nikodym derivative on
Any help would be greatly appreciated!