Additivity of integrals on generalized measure spaces
type: Item
instance of: scholarly article
title: Additivity of integrals on generalized measure spaces
zbMATH Open document ID: 0624.28012
DOI: 10.1016/0097-3165(85)90082-2
author: Julia E. Zerbe
author: Stan Gudder
published in: Journal of Combinatorial Theory. Series A
publication date: 1985-01-01T00:00:00Z
review text: A generalized measure space is a triple (\(\Omega\),\({\mathcal C},\mu)\) where \(\Omega\) is a set of \({\mathcal C}\), a \(\sigma\)-class of subsets of \(\Omega\) closed with respect to disjoint countable unions and complementation and \(\mu\) a measure on \({\mathcal C}\). While in the classical measure theory additivity of integral is an obvious and fundamental result, it is not so in the generalized measure spaces. In general the integral in this case is not additive. The question of the additivity in the case of simple functions is solved in the reviewed paper in a positive way.
Mathematics Subject Classification ID: 28C99
Mathematics Subject Classification ID: 03G12
Mathematics Subject Classification ID: 81P10
Mathematics Subject Classification ID: 81P20
zbMATH DE Number: 4012955
zbMATH Keywords: quantum logic
zbMATH Keywords: generalized measure space
zbMATH Keywords: additivity of integral
MaRDI profile type: Publication
full work available at URL: 0097-3165(85)90082-2
OpenAlex ID: W2041674995
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description: scientific article; zbMATH DE number 4012955