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Math Help - Subsets of Non-Measurable sets

  1. #1
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    Subsets of Non-Measurable sets

    We know there exists a non-measurable subset in [0,1). Call it P.

    P is a non-measurable set constructed by identifying the interval [0,1)
    with the unit circle in R^2. If I can find it online, I'll post a link.

    Let A be a measurable subset of P. Show that A has (Lebesgue) measure 0.


    I must admit I'm stuck as to how to proceed
    Last edited by southprkfan1; March 14th 2010 at 08:57 AM.
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  2. #2
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    Quote Originally Posted by southprkfan1 View Post
    We know there exists a non-measurable subset in [0,1). Call it P.

    P is a non-measurable set constructed by identifying the interval [0,1)
    with the unit circle in R^2. If I can find it online, I'll post a link.

    Let A be a measurable subset of P. Show that A has (Lebesgue) measure 0.


    I must admit I'm stuck as to how to proceed
    The usual proof of the non-measurable set is to prove that it has outer measure 1 and inner measure 0. I like this proof, which contains the result you are looking for.
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