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The multidimensional fundamental theorem of calculus

Part of: Calculus on manifolds; nonlinear operators Real functions Functions of several variables

Published online by Cambridge University Press:  09 April 2009

Washek F. Pfeffer
Washek F. Pfeffer
Affiliation:
Department of MathematicsUniversity of California Davis, California 95616, U.S.A.
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Abstract

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On compact oriented differentiable manifolds, we define a well behaved Riemann type integral which coincides with the Lebesgue integral on nonnegative functions, and such that the exterior derivative of a differentiable (not necessarily continuously) exterior form is always integrable and the Stokes formula holds.

MSC classification

Secondary: 26B20: Integral formulas (Stokes, Gauss, Green, etc.) 58C35: Integration on manifolds; measures on manifolds 26A39: Denjoy and Perron integrals, other special integrals
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 43 , Issue 2 , October 1987 , pp. 143 - 170
Copyright
Copyright © Australian Mathematical Society 1987

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