In the next page he applies this useful theorem:
For applying theorem 6.11 our function must be also bounded but in theorem 6.13 function $f\in\mathcal{R}(\alpha)$ and we have no information about boundedness.
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What is $\mathcal R(\alpha)$? – mathcounterexamples.net Nov 03 '15 at 11:57
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This is the set of all function $f$ that has Stieltjes integral with respect to $\alpha$ over $[a,b]$ – RFZ Nov 03 '15 at 11:59
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3A function which is Stieljes integrable is bounded by definition. – mathcounterexamples.net Nov 03 '15 at 12:02
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Ohh right. Thank you. Sorry for my empty question – RFZ Nov 03 '15 at 12:03
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I do not understand the proof of b). How can we define $c=\pm 1$, plus, where did that last inequality come from? – PLanderos33 Nov 04 '19 at 03:28