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Measurability of a function with finite codomain

  1. Mar 2, 2015 #1
    Hi all,
    I have a simple question as follows:
    [itex]f[/itex] is a function from [itex]X[/itex] to [itex]Y[/itex] where
    [itex]X=[0,1][/itex]; and
    [itex]Y[/itex] is finite, i.e. [itex]\vert Y\vert <\infty[/itex]
    then is [itex]f[/itex] Borel measurable?
    Thank you for your help in advance.
     
  2. jcsd
  3. Mar 2, 2015 #2

    lavinia

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    Why would you think that?
     
  4. Mar 2, 2015 #3

    mathman

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    Let f be the characteristic function of a non-measurable subset of the unit interval. f is not Borel measurable.
     
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