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A Measurable Function not Borel Measurable

  1. Mar 15, 2009 #1
    Most books have the famous example for a Lebesgue measurable set that is not Borel measurable. However, I am trying to find a Lebesgue measurable function that is not Borel measurable. Can anyone think of an example?
  2. jcsd
  3. Mar 15, 2009 #2


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    Use the characteristic function of a set that's Lebesgue but not Borel.
  4. Mar 15, 2009 #3
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