Given two random variables $X$ and $Y$ we know that $E[X|Y] = g(Y)$ where $g$ is a Borel function. Is it a good question to ask under which condition there exists a function $g$ which will be continuous, Lipschitz etc.?
2026-03-31 08:43:43.1774946623
When can one represent the conditional expectation $E[X|Y]$ as $g(Y)$ with continuous $g$?
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