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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| Format: | Article |
| Language: | English |
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Wiley
1992-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171292000905 |
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| _version_ | 1832549038416723968 |
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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). |
| format | Article |
| id | doaj-art-720024b573bf4e7aa5f7961b0a4641a7 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| 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 |