# Help needed about Conditional Expectation

1. Oct 18, 2008

### umutk

I need help about conditional expectation for my research. I get stucked on this point. Could anyone show me how to prove that:
"Let E[|Y|]<∞. By checking that Definition is satisfied, show that if Y is measurable F0, then E[Y|F0]=Y."

Def: Let Y be a random variable defined on an underlying probability space($$\Omega$$,F,P) and satisfying E[|Y|]<∞. Let F0 be a sub-$$\sigma$$-algebra of F. The conditional expected value of Y given F0,denoted E[Y|F0],is an F0-measurable random variable that also satisfies:E[IFY]=E[IFE[Y|F0]] for all F $$\in$$ F0

Note that: Red Fs are sets, but black Fs are sigma-algebras.

I appreciate any response.

2. Oct 18, 2008

### umutk

anybody??

3. Oct 20, 2008

### Pere Callahan

Welcome to PF.
Are you really trying to tell us that is research? To me it sounds like an exercise from a measure theoretic probability course.
I suggest you show what you have tried so far or look up the answer in a text book.