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Math Help - lebesgue measurable set

  1. #1
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    lebesgue measurable set

    let P be a closed set on a finite interval [a,b]. Show that P is Lebesgue measurable.

    i know any closed set is measurable but dont know how to show it. any help would be appreciated.
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  2. #2
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    Hello,

    You have to define a sigma-algebra (of the measurable sets), to which you apply the Lebesgue measure !
    In particular, if the sigma-algebra is the Borel sigma-algebra over [a,b], it's generated by the open subsets of [a,b] (with the usual topology)
    And since a closed set is the complement of an open set, it's still in the Borel sigma-algebra, and hence is measurable.


    As a side note : if one talks about open sets, there must be a definition of the topology you're using. But we'll just assume it's the usual topology...
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