The Stokes theorem for the generalized Riemann integral (Q1852402)
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scientific article; zbMATH DE number 1848865
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Stokes theorem for the generalized Riemann integral |
scientific article; zbMATH DE number 1848865 |
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The Stokes theorem for the generalized Riemann integral (English)
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5 January 2003
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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.
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Stokes theorem
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generalized Riemann integral
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local lipeomorphisms
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