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The fundamental theorem of geometric calculus via a generalized Riemann integral

Alan Macdonald
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Abstract

Using recent advances in integration theory, we give a proof of the fundamental theorem of geometric calculus. We assume only that the tangential derivative $\nabla_VF$ exists and is Lebesgue integrable. We also give sufficient conditions that $\nabla_VF$ exists.

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Alan Macdonald. 1998-07-06. The fundamental theorem of geometric calculus via a generalized Riemann integral. https://arxiv.org/abs/math/9807024

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