I'm having trouble working out a few details from my probability book. It says if P(An) goes to zero, then the integral of X over An goes to zero as well. My book says its because of the monotone convergence theorem, but this confuses me because I thought that has to do with Xn converging to X. Here is my attempt anyway:(adsbygoogle = window.adsbygoogle || []).push({});

We can write the integration as lim n to infinity of E[X(I(An))] = E(lim n to infinity of X P(An)) = E(X(0)) = E(0) = 0.

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# Expectation over Sets

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