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Simple question about Lebesgue and Borel sigma algebra

  1. Nov 25, 2007 #1

    quasar987

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    If N is of null Lebesgue measure. Can we find a Borel set B of null measure such that N is entirely contained in B?
     
  2. jcsd
  3. Nov 25, 2007 #2

    morphism

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    The empty set!
     
  4. Nov 25, 2007 #3

    quasar987

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    it's the other way around. we want B borel such that N is contained in B
     
  5. Nov 27, 2007 #4

    quasar987

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  6. Nov 27, 2007 #5

    morphism

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    Oops!

    This is also true. It follows from the fact that the Lebesgue measure is regular.
     
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