Let $\alpha$ be a monotonically increasing function on $[a,b]$ and $f\in\mathscr{R}(\alpha)$.
I googled it, but i couldn't find a text using relatively easy concepts to prove this. (For example, I don't think dual space concept is necessary to prove this.)
I've seen this theorem quite frequently on this website and it seems it's a very important theorem, so i want to prove it. (I cannot believe why this theorem is not in Rudin's PMA)
Please help me with this proof. Thank you in advance!