# an exercise about lebesgue measure

• October 29th 2013, 05:30 AM
ayrcast
an exercise about lebesgue measure
let $\{E_{n}\}_{n\in\Bbb N}$ be a sequence of measurable subsets such that $E_n \subseteq (0,1)$ and let $\limsup_{n\to\infty} m(E_{n})=1$, prove that $m(\bigcap_{k=1}^\infty E_{k}) > 0$, where m is the measure of Lebesgue.

Any ideas on how to do this?
• October 29th 2013, 08:04 AM
ayrcast
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 $E_{n_{k}}$ such that $m(\bigcap_{k=1}^{\infty}E_{n_{k}})>0$

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