Smoothness conditions on measures using Wallman spaces
In this paper, X denotes an arbitrary nonempty set, ℒ a lattice of subsets of X with ∅,X∈ℒ,A(ℒ) is the algebra generated by ℒ and M(ℒ) is the set of nontrivial, finite, and finitely additive measures on A(ℒ), and MR(ℒ) is the set of elements of M(ℒ) which are ℒ-regular. It is well known that any μ∈M...
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| Format: | Article |
| Language: | English |
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Wiley
1999-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171299227135 |
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| _version_ | 1832550021337186304 |
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| author | Charles Traina |
| author_facet | Charles Traina |
| author_sort | Charles Traina |
| collection | DOAJ |
| description | In this paper, X denotes an arbitrary nonempty set, ℒ a lattice of subsets of X with ∅,X∈ℒ,A(ℒ) is the algebra generated by ℒ and M(ℒ) is the set of nontrivial, finite, and finitely additive measures on A(ℒ), and MR(ℒ) is the set of elements of M(ℒ) which are ℒ-regular. It is well known that any μ∈M(ℒ) induces a finitely additive measure μ¯ on an associated Wallman space. Whenever μ∈MR(ℒ),μ¯ is countably additive. |
| format | Article |
| id | doaj-art-a01966d7a6d7479d8d0a9abbf4ac1bb7 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1999-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-a01966d7a6d7479d8d0a9abbf4ac1bb72025-02-03T06:07:57ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251999-01-0122471372610.1155/S0161171299227135Smoothness conditions on measures using Wallman spacesCharles Traina0St. John's University, Department of Mathematics and Computer Science, 8000 Utopia Parkway, Jamaica 11439, NY, USAIn this paper, X denotes an arbitrary nonempty set, ℒ a lattice of subsets of X with ∅,X∈ℒ,A(ℒ) is the algebra generated by ℒ and M(ℒ) is the set of nontrivial, finite, and finitely additive measures on A(ℒ), and MR(ℒ) is the set of elements of M(ℒ) which are ℒ-regular. It is well known that any μ∈M(ℒ) induces a finitely additive measure μ¯ on an associated Wallman space. Whenever μ∈MR(ℒ),μ¯ is countably additive.http://dx.doi.org/10.1155/S0161171299227135Wallman spacesouter measure associated with a lattice measuresmoothness of a lattice measureregular outer measure. |
| spellingShingle | Charles Traina Smoothness conditions on measures using Wallman spaces International Journal of Mathematics and Mathematical Sciences Wallman spaces outer measure associated with a lattice measure smoothness of a lattice measure regular outer measure. |
| title | Smoothness conditions on measures using Wallman spaces |
| title_full | Smoothness conditions on measures using Wallman spaces |
| title_fullStr | Smoothness conditions on measures using Wallman spaces |
| title_full_unstemmed | Smoothness conditions on measures using Wallman spaces |
| title_short | Smoothness conditions on measures using Wallman spaces |
| title_sort | smoothness conditions on measures using wallman spaces |
| topic | Wallman spaces outer measure associated with a lattice measure smoothness of a lattice measure regular outer measure. |
| url | http://dx.doi.org/10.1155/S0161171299227135 |
| work_keys_str_mv | AT charlestraina smoothnessconditionsonmeasuresusingwallmanspaces |