Some topologies on the set of lattice regular measures

We consider the general setting of A.D. Alexandroff, namely, an arbitrary set X and an arbitrary lattice of subsets of X, ℒ. 𝒜(ℒ) denotes the algebra of subsets of X generated by ℒ and MR(ℒ) the set of all lattice regular, (finitely additive) measures on 𝒜(ℒ).

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Bibliographic Details
Main Author: Panagiotis D. Stratigos
Format: Article
Language:English
Published: Wiley 1992-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Subjects:
Online Access:http://dx.doi.org/10.1155/S0161171292000905
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author Panagiotis D. Stratigos
author_facet Panagiotis D. Stratigos
author_sort Panagiotis D. Stratigos
collection DOAJ
description We consider the general setting of A.D. Alexandroff, namely, an arbitrary set X and an arbitrary lattice of subsets of X, ℒ. 𝒜(ℒ) denotes the algebra of subsets of X generated by ℒ and MR(ℒ) the set of all lattice regular, (finitely additive) measures on 𝒜(ℒ).
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institution Kabale University
issn 0161-1712
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language English
publishDate 1992-01-01
publisher Wiley
record_format Article
series International Journal of Mathematics and Mathematical Sciences
spelling doaj-art-720024b573bf4e7aa5f7961b0a4641a72025-02-03T06:12:21ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251992-01-0115468169510.1155/S0161171292000905Some topologies on the set of lattice regular measuresPanagiotis D. Stratigos0Long Island University, Brooklyn, New York 11201, USAWe consider the general setting of A.D. Alexandroff, namely, an arbitrary set X and an arbitrary lattice of subsets of X, ℒ. 𝒜(ℒ) denotes the algebra of subsets of X generated by ℒ and MR(ℒ) the set of all lattice regular, (finitely additive) measures on 𝒜(ℒ).http://dx.doi.org/10.1155/S0161171292000905lattice; δ and normal lattice; separating and disjunctive lattice; lattice semiseparationmeasure; regularityσ-smoothnessτ-smoothnessand tightness of a measure; tight set of measureslim sup- topology; weak topology; Wallman topology; relative compactnessrepletenessmeasure repletenessand strongly measure repleteness.
spellingShingle Panagiotis D. Stratigos
Some topologies on the set of lattice regular measures
International Journal of Mathematics and Mathematical Sciences
lattice; δ and normal lattice; separating and disjunctive lattice; lattice semiseparation
measure; regularity
σ-smoothness
τ-smoothness
and tightness of a measure; tight set of measures
lim sup- topology; weak topology; Wallman topology; relative compactness
repleteness
measure repleteness
and strongly measure repleteness.
title Some topologies on the set of lattice regular measures
title_full Some topologies on the set of lattice regular measures
title_fullStr Some topologies on the set of lattice regular measures
title_full_unstemmed Some topologies on the set of lattice regular measures
title_short Some topologies on the set of lattice regular measures
title_sort some topologies on the set of lattice regular measures
topic lattice; δ and normal lattice; separating and disjunctive lattice; lattice semiseparation
measure; regularity
σ-smoothness
τ-smoothness
and tightness of a measure; tight set of measures
lim sup- topology; weak topology; Wallman topology; relative compactness
repleteness
measure repleteness
and strongly measure repleteness.
url http://dx.doi.org/10.1155/S0161171292000905
work_keys_str_mv AT panagiotisdstratigos sometopologiesonthesetoflatticeregularmeasures