TITLE: Visualization of Riemann–Stieltjes Integrals
QUESTION [17 upvotes]: The Riemann–Stieltjes integral $\int_a^b f(x)\,dg(x)$ is a generalization of the Riemann integral. It is e.g. heavily used as a starting point for stochastic integration. The approximating Riemann–Stieltjes sums are analogous to the Riemann sums $\sum_{i=0}^{n-1} f(c_i)(g(x_{i+1})-g(x_i))$ where $c_i$ is in the $i$-th subinterval $[x_i,x_{i+1}]$.
The Riemann-sums can be very intuitively visualized by rectangles that approximate the area under the curve.
See e.g. Wikipedia:Riemann sum.
Unfortunately, I cannot find respective intuitive visualizations of the Riemann–Stieltjes sums.
My question: Could anyone provide me with some literature, pictures, links, or especially tools (e.g. Mathematica or even Excel) with which I could play around to get a similar intuition for this more general kind of integral?

REPLY [2 votes]: This article seems useful to me, gives a good overview of existing interpretations:
https://maa.tandfonline.com/doi/abs/10.1080/07468342.2019.1580109?journalCode=ucmj20#.XPJU16WxVkA