Please help me prove: If X,Y∈L1(Ω,F,P) E[X|Y]=Y a.s. , E[Y|X]=X a.s. Then X=Y a.s. I need a detail proof . thank you~!
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Originally Posted by wxxsaber Please help me prove: If X,Y∈L1(Ω,F,P) E[X|Y]=Y a.s. , E[Y|X]=X a.s. Then X=Y a.s. I need a detail proof . You need to try to find one by doing some work for yourself. Please show some effort. BTW what does "a.s." mean?
With your motivation , I'have gave a proof of this problem. Thank you.
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