# Simple functions are dense

#### Fermat

##### Active member
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

Staff member
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.

#### Fermat

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