Let $Y$ be a random variable s.t. $E|Y|<\infty$. Let $E[Y|\mathcal{G}]$ and $Y$ have the same distribution. I need to prove that $E[Y|\mathcal{G}]=Y$ a.s. How does one use the fact that a random variable and its conditional expectation has the same distribution ?
2026-04-07 14:41:27.1775572887
Problem on "Distribution" of conditional expectation w.r.t a sigma field
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