is compact, so has a max on that interval.
Note: This only works in the reals. I notice you have as your space, so I'm not sure this applies, unless you know that closed intervals are compact.
If and , then F is continuous on
Proof so far.
I need to show that , there exists such that whenever where , then I will have
Now, I know have that
Since f is integrable, this integral exists, but how should I refine it so it is less than ?