1. ## 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.

Any ideas on how to do this?

2. ## 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.