A constructive definition of the \(n\)-dimensional \(\nu(S)\)-integral in terms of Riemann sums
type: Item
instance of: scholarly article
title: A constructive definition of the \(n\)-dimensional \(\nu(S)\)-integral in terms of Riemann sums
zbMATH Open document ID: 0870.26004
author: Dirk Jens F. Nonnenmacher
published in: Real Analysis Exchange
publication date: 1997-08-27T00:00:00Z
review text: Introduced by Nonnenmacher and Jurkat as a descriptive integral (i.e., in terms of an additive almost everywhere differentiable set function), the \(\nu(S)\)-integral is a non-absolutely convergent integral in \(\mathbb{R}^n\) which allows to integrate the divergence of differentiable vector fields over quite general sets. The present paper proposes an equivalent definition based upon Riemann sums and proves that every function which is variationally integrable in the sense of Pfeffer is \(\nu(S)\)-integrable and that both integrals coincide.
Mathematics Subject Classification ID: 26B20
Mathematics Subject Classification ID: 26A42
Mathematics Subject Classification ID: 26B15
zbMATH DE Number: 878216
zbMATH Keywords: Gauge integrals
zbMATH Keywords: descriptive integral
zbMATH Keywords: \(\nu(S)\)-integral
zbMATH Keywords: non-absolutely convergent integral
zbMATH Keywords: Riemann sums
reviewed by: Jean Mawhin
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 878216