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.