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Math Help - Hamel basis

  1. #1
    Junior Member
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    Hamel basis

    I need to prove that no Hamel basis can contain a set of positive measure. I already know that a measurable Hamel basis is of Lebesgue zero measure, but I don't how to you use this.
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  2. #2
    Super Member
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    Re: Hamel basis

    A basis for what? If the space is finite dimensional a Hamel basis is finite so it has measure zero (and every subset is finite so...). If the space is infinite dimensional you'll have to specify what measure you're using.
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  3. #3
    Junior Member
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    Re: Hamel basis

    A Hamel basis is a basis of R over Q. The question is respect to Lebesgue measure.
    Thanks.
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