# Lebesgue Integral Question

1. Apr 6, 2010

1. The problem statement, all variables and given/known data
For sets E,F $$\in$$ L, show that χ_E = χ_F almost everywhere if and only if µ(EΔF) = 0

where χ_E is the characteristic function w.r.t. E
and µ(EΔF) is the lebesgue measure of the symmetric difference of E and F
and L is the set of lebesgue measurable sets

2. Relevant equations

A property about real numbers holds almost everywhere if the set of x where it fails to be true has Lebesgue measure 0.

3. The attempt at a solution

I'm really stuck on this. I'm not asking anyone to do it for me, but if anyone could please give me a point in the right direction, that would be great thanks!

2. Apr 6, 2010

### Dick

Isn't the set where the characteristic function of E and F differ equal to the symmetric difference of E and F?