On additivity of mappings on measurable functions
type: Item
instance of: scholarly article
title: On additivity of mappings on measurable functions
zbMATH Open document ID: 1306.28001
DOI: 10.1134/S0037446614010029
published in: Siberian Mathematical Journal
publication date: 2014-11-04T00:00:00Z
review text: Let \(\mathcal{K}\) be a hereditary cone in \(\mathfrak{M}^+\), where \(\mathfrak{M}=\mathfrak{M}(\Omega)\) is a vector space of measurable functions on \(\Omega\). The main result of the paper is the following. Let \(T:\mathcal{K}\rightarrow [0,\infty]\). Then, \(T\) is additive if and only if \(T\) is \(l\)-additive and regular. Moreover, the paper under review describes the relation between \(l\)-additive and monotone maps and the last section contains partial characterization of subadditive mappings.
reviewed by: Przemysław Górka
Mathematics Subject Classification ID: 28A20
Mathematics Subject Classification ID: 39B62
zbMATH DE Number: 6365596
zbMATH Keywords: measure space
zbMATH Keywords: additive maps
zbMATH Keywords: vector lattice
author: Airat Bikchentaev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6365596