Let X be integrable and $A_n$ a sequence of subsets such that $ \lim_{n\to \infty} {P(A_n)} =0$. Show that $E X 1_{A_n} \to 0$.
Integrable Functions in Probability
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probability
measure-theory
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1Dear 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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0What is $X$???? – 2012-10-17
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0Yes 1An the indicator function of An. Sorry I am not used to TeX commands. – 2012-10-17
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0The $X$ has disappeared from the expectation??? – 2012-10-17