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