Let $E,E_n \subset \mathbb{R}^N$ be measurable such that $E_n \subset E, E$ is bounded domain, $E_{n+1} \subset E$ and $\lim_{n\rightarrow \infty}L^N(E_n) = 0$. Are there $K_n$ compact such that $E_n \subset K_n \subset E$ and $\lim_{n\rightarrow \infty}L^N(K_n)=0$?
$L^N(A)$ denotes the $N$-dimensional Lebesgue measure of $A$.