The Stokes theorem for the generalized Riemann integral
type: Item
instance of: scholarly article
title: The Stokes theorem for the generalized Riemann integral
zbMATH Open document ID: 1023.26010
published in: Real Analysis Exchange
publication date: 2003-01-05T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 26B20
zbMATH DE Number: 1848865
zbMATH Keywords: Stokes theorem
zbMATH Keywords: generalized Riemann integral
zbMATH Keywords: local lipeomorphisms
author: Washek F. Pfeffer
reviewed by: Jean Mawhin
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1848865