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Math Help - lebesgue measure

  1. #1
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    lebesgue measure

    Let P be a closed set on a finite interval [a,b]
    a) prove P is a Lebesgue measurable
    b)Suppose its lebesgue measure m(P)=0. is it true that P is countable? Prove or give a counter example.

    since borel set is measurable, i dont think it is that hard to prove a)
    but i dont know how to do b). would someone help me on this please?
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  2. #2
    Senior Member Shanks's Avatar
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    A counterexample: Cantor set is a set with measure 0 but uncountable.
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