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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The general form of Green's theorem


Authors: W. B. Jurkat and D. J. F. Nonnenmacher
Journal: Proc. Amer. Math. Soc. 109 (1990), 1003-1009
MSC: Primary 26B20
DOI: https://doi.org/10.1090/S0002-9939-1990-1000158-3
MathSciNet review: 1000158
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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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DOI: https://doi.org/10.1090/S0002-9939-1990-1000158-3
Keywords: Green's theorem, Cauchy's integral theorem
Article copyright: © Copyright 1990 American Mathematical Society