I've seen a lot of excellent visual material (gifs, pictures) here, in topics like this, and I used many of them to understand/explain concepts (particularly gifs showing Riemann sums or fourier series), and now I'm looking for material of this kind for the Riemann-Stieltjes integral.

Any kind would be appreciated.


2 Answers 2


I had the same problem at some point, and I could not find much around. After a bit, I found the following.

  • Here you find a mathoverflow question on the very same topic, where you find some explanations and some pictures;

  • Also, you should really try to find the article "A Geometric Interpretation of the Riemann-Stieltjes Integral", by Gregory L. Bullock (you find the jstor page of that article in Sahadeo Padhye's answer in the previous link). Actually, if you read it, I am sure you will find everything you need (it is a very nice article).

I hope these references will be helpful.

  • $\begingroup$ have you seen the following paper arxiv.org/pdf/math/0110241 $\endgroup$
    – Jean Marie
    Commented Mar 6, 2016 at 22:38
  • $\begingroup$ No, but I will take a look. $\endgroup$
    – Kolmin
    Commented Mar 6, 2016 at 22:40

Grobler, T. (2019). Visualization of the Riemann–Stieltjes Integral. The College Mathematics Journal, 50(3), 198-209.


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