A Measurable Function not Borel Measurable

[zling110]

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?

 

[dvs]

Use the characteristic function of a set that's Lebesgue but not Borel.

 

[zling110]

Use the characteristic function of a set that's Lebesgue but not Borel.

thanks