Real Analysis Exchange

The Stokes Theorem for the Generalized Riemann Integral

W. F. Pfeffer

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In $\mathbb{R}^m$, we define the generalized Riemann integral over normal $m$-dimensional currents with compact support and bounded multiplicities, and prove the Stokes theorem for continuous $(m-1)$-forms that are pointwise Lipschitz outside sets of $\sigma$-finite $(m-1)$-dimensional Hausdorff measure. In addition, we show that the usual transformation formula holds for local lipeomorphisms, which need not be injective

Article information

Real Anal. Exchange, Volume 26, Number 2 (2000), 623-636.

First available in Project Euclid: 27 June 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 49Q15: Geometric measure and integration theory, integral and normal currents [See also 28A75, 32C30, 58A25, 58C35] 28A75: Length, area, volume, other geometric measure theory [See also 26B15, 49Q15]
Secondary: 26B15: Integration: length, area, volume [See also 28A75, 51M25]

BV sets functions local lipeomorphisms top-dimensional normal currents


Pfeffer, W. F. The Stokes Theorem for the Generalized Riemann Integral. Real Anal. Exchange 26 (2000), no. 2, 623--636.

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