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Homework Help: Lebesgue Integral Question

  1. Apr 6, 2010 #1
    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!
  2. jcsd
  3. Apr 6, 2010 #2


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