Can You Visualize the Riemann-Stieltjes INTEGRAL?

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[sphakamisozondi]

I'm starting to think, Riemann is a criminally underrated mathematician by the general public.

[gavintillman]

I find this concept, and the related Radon Nikodym derivatibe unintuitive - this helps. One area where the motivation works better is in probabily theory where the ingegral of g(x) dF(x) where F is cumulative proabality function is the integral g(x) f(x) where f(x) is the probability density function - namely the expectation of g(x)

[pandabers]

Thanks for this! I encountered some integrals with respect to a function in probability but was not familiar with these. So is it correct to say that if f(x) = x, they the integral of x with respect to g(x) is the area under g-inverse(x)?

[randomdude]

If the function g is a parameterization of a curve, then wouldn't the Riemann-Stieltjes integral become a line integral? Would it be incorrect to interpret the line integral as a special case of the Riemann-Stieltjes integral?

[apolloandartemis]

Hi! How does this relate to the geometric intuition behind u-sub?

[JOHN-exrb]

pretty nice moring
i hope this wont get me although keep these things up