Equivalence of Brooks-Jewett, Vitali-Hahn-Saks and Nikodým convergence theorems for uniform semigroup-valued additive functions on a Boolean ring
type: Item
instance of: scholarly article
title: Equivalence of Brooks-Jewett, Vitali-Hahn-Saks and Nikodým convergence theorems for uniform semigroup-valued additive functions on a Boolean ring
zbMATH Open document ID: 0612.28006
author: Pedro Morales
author: Paolo De Lucia
published in: Ricerche di Matematica
publication date: 1986-01-01T00:00:00Z
review text: For sequences of strongly bounded additive functions from a Boolean ring \({\mathcal R}\) having the subsequential interpolation property into a Hausdorff uniform commutative semigroup S, the authors prove the Brooks- Jewett theorem and show that the Brooks-Jewett theorem is equivalent with the Vitali-Hahn-Saks theorem and the Nikodým convergence theorem. In the case where \({\mathcal R}\) is a \(\sigma\)-ring of sets and S is a Hausdorff topological commutative group, the reslt is due to \textit{L. Drewnowski} [Bull. Acad. Pol. Sci., Sér. Sci. Math. Astron. Phys. 20, 725-731 (1972; Zbl 0243.28011)].
Mathematics Subject Classification ID: 28B10
Mathematics Subject Classification ID: 28A60
zbMATH DE Number: 3989691
zbMATH Keywords: semigroup-valued additive functions
zbMATH Keywords: strongly bounded additive functions
zbMATH Keywords: Brooks-Jewett theorem
zbMATH Keywords: Vitali-Hahn-Saks theorem
zbMATH Keywords: Nikodým convergence theorem
reviewed by: Klaus D. Schmidt
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3989691