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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!

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    @copper.hat I think you are right. I think hypothesis should be rephrased as '$\alpha,f$ are discontinuituous at the same side' and proof for this is relatively easy to me. Thank you!2012-12-24

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