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Given a measurable space $(X, V, m)$ and $\{F_{n}\}_{1}^{\infty}\subset $ $V $ is a sequence of sets such that $m(F_{n})\leq$ $e^{-n}$ $\forall {n}.$ show that the functions $h(x)=\sum_{1}^{\infty} { \chi_E{_n}(x)}$ and $g(x)=\sum_{1}^{\infty} {n^{t}\chi_E{_n}(x)}$ belongs to $L^p $ for all $ 0

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    Is $E^n = F_n$?2011-11-12
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    Instead of [deleting](http://math.stackexchange.com/questions/81381/integration-measure) your old question, you could have edited the old one. This would have bumped it to the front page. At that opportunity you could also have gotten rid of the typos that were already pointed out to you.2011-11-12
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    @ t.d, I wanted to make use of the definition of L^p, that was why I deleted the other equations.2011-11-12

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