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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.2012-12-21
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    Skip the chapter.2012-12-21
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    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?2012-12-22
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    It can be convenient in analytic number theory.2012-12-22
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    @Eric: I'd be interested to hear about that, could you please expand that into an answer?2012-12-22

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