# Homework Help: Measure/Uniform Convergence

1. Apr 17, 2012

### EV33

1. The problem statement, all variables and given/known data

I would just like to be pointed in the right direction. I have this theorem:

Let E be a measurable set of finite measure, and <fn> a sequence of measurable functions that converge to a real-valued function f a.e. on E. Then given ε>0 and $\delta$>0, there is a set A$\subset$E with mA<$\delta$, and an N such that for all x$\notin$A and all n≥N,
lfn(x)-f(x)l<ε

To me it appears to be concluding:
Given ε>0 and $\delta$>0, there is a set A$\subset$E with mA<$\delta$, and an N such that for all x$\notin$A and all n≥N,
<fn> converges uniformly to a real-valued function f on E~A.

I know that this isn't case but I don't see why. So my question is what would the conclusion of this theorem need to say, in terms of ε and $\delta$, so that <fn> converges uniformly to a real-valued function f on E~A?