Uniform \(s\)-boundedness and convergence results for measures with values in complete l-groups

DOI10.1006/jmaa.2001.7715zbMath1006.28012OpenAlexW2005096337MaRDI QIDQ5957146

Domenico Candeloro, Antonio Boccuto

Publication date: 9 March 2003

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmaa.2001.7715

zbMATH Keywords

convergence\(s\)-boundednessdistributive lattice groupsl-group valued measuresmeasure extension

Mathematics Subject Classification ID

Set functions, measures and integrals with values in ordered spaces (28B15)

Related Items (14)

Limit theorems in \((l)\)-groups with respect to \((D)\)-convergence ⋮ Unnamed Item ⋮ Life and work of Domenico Candeloro: an appreciation ⋮ Modular \(\mathrm{d}_0 \)-algebras ⋮ Some remarks on Vainikko integral operators in BV type spaces ⋮ Filter convergence and decompositions for vector lattice-valued measures ⋮ Ideal convergence and divergence of nets in (ℓ)-groups ⋮ Abstract theorems on exchange of limits and preservation of (semi)continuity of functions and measures in the filter convergence setting ⋮ Uniform \((s)\)-boundedness and regularity for \((l)\)-group-valued measures ⋮ Unnamed Item ⋮ Equivalence between limit theorems for lattice group-valued \(k\)-triangular set functions ⋮ Dieudonné-type theorems for lattice group-valued k-triangular set functions ⋮ On locally solid topological lattice groups ⋮ Some further results on ideal summability of nets in (\(\ell\)) groups

Cites Work

• Compactness in spaces of group-valued contents, the Vitali-Hahn-Saks theorem and Nikodým's boundedness theorem
• Equivalence of Brooks-Jewett, Vitali-Hahn-Saks and Nikodým convergence theorems for uniform semigroup-valued additive functions on a Boolean ring
• The Nikodým boundedness theorem for lattice-valued measures
• Representations of Archimedean Riesz spaces. - A survey
• Brooks-Jewett and Nikodym convergence theorems for orthoalgebras that have the weak subsequential interpolation property
• The measure extension problem for vector lattices
• Equicontinuous sets of measures and applications to Vitali's integral convergence theorem and control measures
• Boolean algebras with pathological order topologies
• A Direct Proof of the Matthes-Wright Integral Extension Theorem
• Stone-Algebra-Valued Measures and Integrals
• ON THE VITALI-HAHN-SAKS AND NIKODÝM THEOREMS
• On Finitely Additive Vector Measures
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