Are Simple Functions Dense in Bounded Borel Functions on a Compact Space?

[Fermat1]

Let K be a compact space and let B be the space of bounded borel functions on K equipped with the supremum norm. Show that simple functions (i.e. functions attaining only a finite number of values) are dense in B.

Thanks

 

[Jameson]

Let K be a compact space and let B be the space of bounded borel functions on K equipped with the supremum norm. Show that simple functions (i.e. functions attaining only a finite number of values) are dense in B.

Thanks

Hi Fermat,

Please make an effort and show us what you've done.

Thanks.

 

[Fermat1]

I know I need to show $||f_{n}-f||->0$ where the $f_{n}$ are simple but I don't know where to start

 

[ThePerfectHacker]

I think this would do it,
Show simple functions are dense