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Math Help - condition expection question

  1. #1
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    Tianjin
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    condition expection question

    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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  2. #2
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    Re: condition expection question

    Quote Originally Posted by wxxsaber View Post
    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?
    Thanks from LimpSpider
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  3. #3
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    Re: condition expection question

    With your motivation , I'have gave a proof of this problem. Thank you.
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