1. Let f be a nonnegative measurable function on . Show that if is defined by then F is continuous on .

I know that to prove that a function is continuous, you have to show that for any open set so that is open, but I'm not sure what to do from there.

2. Let f be a nonnegative measurable function on a measurable set E with . Prove that for each there exists such that for every measurable set with we have

I am clueless how to even start this problem.