# What is the point of Riemann-Stieltjes integration?

My book on complex analysis dedicates an entire chapter to this integral in order to motivate/define complex line integrals. Having spent a semester on integration theory, I am not to keen on learning about yet another integral when I am perfectly satisfied with the Lebesgue integral. My understanding is that the Riemann-Stieltjes integral is just a generalization of the Riemann integral. I simply don't see why I need it for this course or why I would ever need it at all. Some insight would be greatly appreciated.

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Probability is an area that uses it often. –  toypajme Dec 21 '12 at 23:33
Skip the chapter. –  Qiaochu Yuan Dec 21 '12 at 23:39
There is a point to Riemann-Stieltjes integration, but the point is fairly far away from complex line integrals. As Qiaochu says, it is very likely that this material can be safely skipped. What is the text? –  Pete L. Clark Dec 22 '12 at 1:46
It can be convenient in analytic number theory. –  Eric Naslund Dec 22 '12 at 4:39
@Eric: I'd be interested to hear about that, could you please expand that into an answer? –  user5501 Dec 22 '12 at 4:54

I see it the complete other way around: The Lebesgue-Stieltjes integral is a special case of the Lebesgue integral. And as the Wikipedia page notes: "The Lebesgue-Stieltjes integral $\int_a^b f(x) \,dg(x)$ is defined as the Lebesgue integral of $f$ with respect to the measure $μ_g$ in the usual way." –  kahen Dec 22 '12 at 12:55