Is there any newly written textbook that discusses the Riemann-Stieltjes integral from the same perspective as in Chap. 6 in the book Principles of Mathematical Analysis by Walter Rudin, 3rd edition?

I've got the book Mathematical Analysis by Tom M. Apostol, 2nd edition, and Calculus volumes 1 & 2, 2nd edition, also by the same author. But neither of these, it apperas to me, discusses integration using the same approach as has been adopted by Rudin.

  • $\begingroup$ The Elements of Real Analysis by Bartle discusses it. Not sure if that's as exhaustive as you would want. Riemann-Stieltjes are probably best discussed in the context of Lebesgue Measure where Riemann-Stieltjes gives you a concrete way to realize the regular measures on the reals. $\endgroup$ – Robert Wolfe Jun 2 '18 at 4:28
  • $\begingroup$ Rudin's perspective on Riemann-Stieltjes integrals is essentially limited to the case of a monotonic integrator and says about all there is to be said. Why would you look for another book like it? Apostol, on the other hand, ranges farther on the topic including integrators of bounded variation. $\endgroup$ – RRL Jun 2 '18 at 21:11

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