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The parametric Gauss-Green theorem. (English) Zbl 0603.30047
A strong parametric Gauss-Green theorem, for chains homologous to zero in a plane region, follows directly from an interchange in order of integrations.
MSC:
30E20 Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane
30A99 General properties of functions of one complex variable
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References:
[1] John D. Dixon, A brief proof of Cauchy’s integral theorem, Proc. Amer. Math. Soc. 29 (1971), 625 – 626. · Zbl 0205.37801
[2] Herbert Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer-Verlag New York Inc., New York, 1969. · Zbl 0176.00801
[3] J. H. Michael, An approximation to a rectifiable plane curve, J. London Math. Soc. 30 (1955), 1 – 11. · Zbl 0064.31102 · doi:10.1112/jlms/s1-30.1.1 · doi.org
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