# If $\mu$ is $\sigma$ finite and $f_n \rightarrow f$ a.e then $f_n \rightarrow f$ uniformly on each $E_j$

If $\mu$ is $\sigma$ finite and $f_n \rightarrow f$ a.e, there exists $E_1,E_2, \ldots \subset X$ such that $\mu((\bigcup_{1}^{\infty}E_j)^{c})=0$ and $f_n \rightarrow f$ uniformly on each $E_j$