# Measurability of a function with finite codomain

1. Mar 2, 2015

### 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?

2. Mar 2, 2015

### lavinia

Why would you think that?

3. Mar 2, 2015

### mathman

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