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I'm working through an analysis text independently to prepare for grad school, and the author has discussed the limitations of both the Riemann and Lebesgue integrals and only hinted at the power of generalized Riemann integral which I had to look into upon hearing about it.

Given the power of differential forms for integration and analysis on manifolds, have there been any treatments of the theorems of vector calculus that incorporate both the convenience of differential forms and the supposed power of the Henstock-Kurzweil integral? One would think that the two combined would make for a powerful analytical punch so to speak. If so, could anyone recommend a reference for such a work?

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I think you might find this interesting:

http://faculty.luther.edu/~macdonal/Stokes.pdf

It's a paper that proves a version of Strokes' theorem (more general than the usual one) using the HK integral.

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