need help with the following


m(E) represents the measure of E and m^*(E) represents the outer measure of E

the sigma in q1 represent the cesaro sums and K_n is fejers kernel.

if anyone can help me with these id really appreciate itt. will possibly buy fg to give u if sufficient help given

Don't need to send fg.

ad 9:
Write E_n = {e \in E | f(e) >= 1/n)}
Then obviously
0 = \int_E f >= \int_{E_n} f >= m(E_n) * 1/n
and so m(E_n) = 0.
The argument is complete if you write
E = \cup_{n natural} E_n
i.e. E is the countable union of null sets E_n.

ad 17: I'll see if I have an idea. My knowledge about measure theory is quite limited.

ad 1: I'm afraid I can't help you with this one. Don't know about Cesaro sums etc.