The general form of Green’s theorem

Jurkat, W. B.; Nonnenmacher, D. J. F.

doi:10.1090/S0002-9939-1990-1000158-3

The general form of Green’s theorem
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by W. B. Jurkat and D. J. F. Nonnenmacher PDF

Proc. Amer. Math. Soc. 109 (1990), 1003-1009 Request permission

Abstract:

Using a recently developed Perron-type integration theory, we prove a new form of Green’s theorem in the plane, which holds for any rectifiable, closed, continuous curve under very general assumptions on the vector field. In particular, Cauchy’s integral theorem can be deduced in its presently most general form.

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