Proving Equality of Characteristic Functions using Lebesgue Measure?

[Pyroadept]

Homework Statement

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

Homework Equations

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

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!

 

[Dick]

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