help on a proof

Hi, all,

I have a question on how to prove E(sup_n(Y_n)) < infinity.
Known: (1) Y_n >=0 is random variables and bounded for any n
(n=1,2,...);
(2) lim_{n->infinity} Y_n = 0;
Question: can we prove: E(sup_n(Y_n)) < infinity?

Thanks a lot,
Cloud

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