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Math Help - lebesgue measurable set construction

  1. #1
    Senior Member Shanks's Avatar
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    lebesgue measurable set construction

    Construct a lebesgue measurable set S such that for any nonempty interval I, 0< m(S\cap I)< m(I),
    where m is the lebesgue measure in real line.
    Is it possible that S has finite lebesgue measure?
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  2. #2
    Senior Member Shanks's Avatar
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    .>-<. Any1 help me please.
    Open to any solution or idea.
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