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Simple functions are dense

Fermat

Active member
Nov 3, 2013
188
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

Administrator
Staff member
Jan 26, 2012
4,041
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
Nov 3, 2013
188
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

Well-known member
Jan 26, 2012
236