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## Homework Statement

For sets E,F [tex]\in[/tex] 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!