I need help about conditional expectation for my research. I get stucked on this point. Could anyone show me how to prove that:(adsbygoogle = window.adsbygoogle || []).push({});

"Let E[|Y|]<∞. By checking thatis satisfied, show that if Y is measurable FDefinition_{0}, then E[Y|F_{0}]=Y."

Let Y be a random variable defined on an underlying probability space([tex]\Omega[/tex],F,P) and satisfying E[|Y|]<∞. Let FDef:_{0}be a sub-[tex]\sigma[/tex]-algebra of F. The conditional expected value of Y given F_{0},denoted E[Y|F_{0}],is an F_{0}-measurable random variable that also satisfies:E[I_{F}Y]=E[I_{F}E[Y|F_{0}]] for all F [tex]\in[/tex] F_{0}

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

I appreciate any response.

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# Help needed about Conditional Expectation

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