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Recently I was looking for some source for exercises in Riemann-Stieltjes integral and going through several calculus books (Hunt, Edwards, Thomas, Adams) I found no such exercises. Is there any exercise\problem book which covers Riemann-Stieltjes integral?

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They come up naturally in some parts of Analytic Number Theory, so you might look for a textbook on that subject, Apostol or Shapiro or some other. – Gerry Myerson May 31 '12 at 10:55

Chapter 7 of T.M. Apostol's "Mathematical Analysis" has a good deal both of theory and exercises about the R.S. integral.

Also R.G. Bartle's "The Elements of Real Analysis", section 22, chapter VI, has many examples and exercises.

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Chapter 2 of Zygmund and Wheeden's "Measure and Integral" has some exercises regarding the Riemann-Stieltjes integral.

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This book begins the study of the integral from the general Riemann-Stieltjes Integral. The topic is covered adequately as would be expected from an undergraduate introductory text on real analysis. There are a good number of exercises at the end of the chapter.

I hope this was helpful.

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