Can you find an example where E(E(X|F)|G) $\neq$ E(E(X|G)|F) (F and G is $\sigma$-field in probability theory)
2026-03-26 07:33:15.1774510395
Example of E(E(X|F)|G) \neq E(E(X|G)|F)
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Try an example with $F$ and $G$ the $\sigma$-algebras generated by random variables $Y,Z$ respectively. $\mathbb E[\ldots|F]$ is a function of $Y$ and $\mathbb E[\ldots|G]$ is a function of $Z$. Except in "trivial" cases, these won't be equal.