Let ${f_n}$ be a sequence of measurable functions on E that converges to the real valued f pointwise on E. Show that $E=\bigcup_{k=1}^{\infty}E_k$, where for each k, $E_k$ is measurable, and ${f_n}$ converges uniformly to $f$ on each $E_k$ if $k>1$ and $m(E_1)=0$.
I have been stuck in this problem for a while now i do not know where to even begin or what to look for exactly, if anyone can provide some guidance that will be great