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Lebesgue Integral Question

  • Thread starter Pyroadept
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  • #1
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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!
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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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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