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The Stokes theorem for the generalized Riemann integral. (English) Zbl 1023.26010

In this paper, the author defines in \({\mathbb R}^m\) a generalized Riemann integral over \(m\)-dimensional currents with compact support and bounded multiplicities. He then proves in this setting the Stokes theorem for continuous \((m-1)\)-forms that are pointwise Lipschitz outside sets of \(\sigma\)-finite \((m-1)\)-dimensional Hausdorff measure. For such an integral, the usual transformation formula is also proved for local lipeomorphisms, not necessarily injective.

MSC:

26B20 Integral formulas of real functions of several variables (Stokes, Gauss, Green, etc.)
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