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Help needed about Conditional Expectation

  1. Oct 18, 2008 #1
    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([tex]\Omega[/tex],F,P) and satisfying E[|Y|]<∞. Let F0 be a sub-[tex]\sigma[/tex]-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 [tex]\in[/tex] F0

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

    I appreciate any response.
     
  2. jcsd
  3. Oct 18, 2008 #2
    anybody??
     
  4. Oct 20, 2008 #3
    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.
     
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