New results on integration on the Levi-Civita field
type: Item
instance of: scholarly article
title: New results on integration on the Levi-Civita field
zbMATH Open document ID: 1300.26019
author: Khodr Shamseddine
published in: Indagationes Mathematicae. New Series
publication date: 2013-01-03T00:00:00Z
review text: The Levi-Civita field \(\mathcal R\) consists of functions \(f: \mathbb Q\to \mathbb R\) whose supports are left-finite, that is there is only a finite set of support points to the left of any given one. The paper is a continuation of an earlier one, by \textit{K. Shamseddine} and \textit{M. Berz} [Contemp. Math. 319, 369--387 (2003; Zbl 1130.12301)], devoted to the integration theory for \(\mathcal R\)-valued functions on subsets of \(\mathcal R\). The author proves that the integrals of functions coinciding almost everywhere are equal and that the uniform convergence preserves the measurability of functions and the values of their integrals. Thus main properties of integrals over \(\mathcal R\) are similar to those of the classical counterparts.
reviewed by: Anatoly N. Kochubei
Mathematics Subject Classification ID: 26E30
Mathematics Subject Classification ID: 12J25
Mathematics Subject Classification ID: 28A20
Mathematics Subject Classification ID: 46S10
zbMATH DE Number: 6121469
zbMATH Keywords: Levi-Civita field
zbMATH Keywords: measurable functions
zbMATH Keywords: integral
zbMATH Keywords: uniform convergence
MaRDI profile type: Publication
full work available at URL: j.indag.2012.08.005
OpenAlex ID: W2025630631
DOI: 10.1016/J.INDAG.2012.08.005
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description: scientific article; zbMATH DE number 6121469