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Thread: an exercise about lebesgue measure

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    an exercise about lebesgue measure

    let $\displaystyle $\{E_{n}\}_{n\in\Bbb N}$$ be a sequence of measurable subsets such that $\displaystyle $E_n \subseteq (0,1)$$ and let $\displaystyle $\limsup_{n\to\infty} m(E_{n})=1$$, prove that $\displaystyle $m(\bigcap_{k=1}^\infty E_{k}) > 0$$, where m is the measure of Lebesgue.


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  2. #2
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    Re: an exercise about lebesgue measure

    P.S. there was an errata corrige on the book, the exercise asks to prove that exists a subsequence $\displaystyle E_{n_{k}}$ such that $\displaystyle m(\bigcap_{k=1}^{\infty}E_{n_{k}})>0$

    Sorry for the double post. I found it only now.
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