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Let X be integrable and $A_n$ a sequence of subsets such that $ \lim_{n\to \infty} {P(A_n)} =0$. Show that $E X 1_{A_n} \to 0$.

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    Dear Kamini, your question is not clear, probably there are some typos. Is $F=X$? Is $1A_n$ the indicator function of $A_n$? in this case I think it is better to write $1_{A_n}$.2012-10-17
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    What is $X$????2012-10-17
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    Yes 1An the indicator function of An. Sorry I am not used to TeX commands.2012-10-17
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    The $X$ has disappeared from the expectation???2012-10-17

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