J Austral Math Soc Ser A 43 pp143--170, 1987.

The Multidimensional Fundamental Theorem of Calculus

Washek F. Pfeffer

Abstract

On compact oriented differentiable manifolds, we define a well behaved Riemann type integral which coincides with the Lesbesgue 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.

1980 AMS Subject Classification: primary 26B20, 58C35; secondary 26A39

Browse the article

Authors

Washek F. Pfeffer

Department of Mathematics, University of California, Davis, California 95616, U.S.A.