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# Visualisation of Riemann-Stieltjes-Integrals

The Riemann-Stieltjes-Integral $\int_a^bf(x)dg(x)$ 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 analog 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 esp. 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.