## Lebesgue Integral

Suppose for all $n \in \mathbb{N}$, we have $f_n \in L^p(X)$ where $m(X) < \infty$.
Prove that for every $\epsilon>0$ , there exists a set $E$ of finite measure, such that for all $n \in \mathbb{N}$ , $\int_{E^c} |f_n|^p \, dm < \epsilon$.