Answer by Zhanxiong for Does independence almost everywhere imply independence?
Yes, you can conclude that.First, by the defining relation of conditional probability $P(X \in A | Y)$, for any Borel set $B$, we have\begin{align*}\int_{\{Y \in B\}}P(X \in A | Y) dP = P(X \in A, Y...
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Let be $X$ and $Y$ two random variables such that, for any event $A$,$P( X \in A \mid Y) = P(X\in A)$ with probability 1.Can I conclude that $X$ and $Y$ are independent ?
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