🚀 go-pugleaf

I am interested in mean square convergence as it applies to random variables.  
My specific query is this:

Given: Let X_n n=1,2,3,... and X be random variables. And suppose that the  
sequence X_n converges in mean square to X, that is

lim_(n->infinite) E{ (X_n - X)^2 } = 0

Hypothesis: lim_(n->infinite) E{ X_n } = E{ X }

I am not sure this is true or under what conditions it might be true. I would  
appreciate any enlightenment on this matter you can provide. I have searched  
books by Papoulis, Shanmugan, W. Gardner, and Davenport without success.

Please reply directly (I do not normally read this newsgroup). If there is  
sufficient interest, I will summarize to the net. Thanks!

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Dennis W. Ruck               Air Force Institute of Technology
druck@afit.af.mil            Wright-Patterson AFB, Ohio
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