Perhaps if i write then
then it would be true that if f is integrable then it is also square integrable... does this seem plausible?
If is bounded, and E is of finite measure, i.e , (m here is the lebesgue measure but it can be arbitrary).
Is ?
Is it enough to say:
since for some real M.
But what I dont get is that this argument only uses the fact f is bounded, not the fact that f is integrable.
I know that since E is of finite measure. I wonder if this has something to do with the answer?