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
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!