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How do you prove that if X converges in probability and expectation that this implies convergence in mean? I think I have to use Chebyshev's Inequality, but am not sure how to incorporate the expectation convergence. Thanks

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    What is the difference between convergence in expectation and convergence in mean?2012-11-08
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    Xn--> X in l1 is convergence in mean, and E[Xn]--> E[X] is convergence in expectation. Sorry I don't know of a good way to type this in using Latex.2012-11-08
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    Beware that your terminology is somewhat non standard. Anyway, the result does not hold, see my answer.2012-11-09

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