Measurability of a function with finite codomain

[hwangii]

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

 

[lavinia]

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

Why would you think that?

 

[mathman]

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