Measurability of a function with finite codomain

  • Thread starter hwangii
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  • #1
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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.
 

Answers and Replies

  • #2
lavinia
Science Advisor
Gold Member
3,248
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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.
Why would you think that?
 
  • #3
mathman
Science Advisor
7,955
498
Let f be the characteristic function of a non-measurable subset of the unit interval. f is not Borel measurable.
 

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