On finitely subadditive outer measures and modularity properties
Let ν be a finite, finitely subadditive outer measure on P(X). Define ρ (E)=ν (X)−ν (E′) for E⊂X. The measurable sets Sν and Sρ and the set S={E⊂X/ν (E)=ρ (E)} are investigated in general, and in the presence of regularity or modularity assumptions on ν. This is also done for ν0(E)=inf{ν (M)/E⊂...
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| Format: | Article |
| Language: | English |
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Wiley
2003-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171203208115 |
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| _version_ | 1850179100958785536 |
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| author | Charles Traina |
| author_facet | Charles Traina |
| author_sort | Charles Traina |
| collection | DOAJ |
| description | Let ν be a finite, finitely subadditive outer measure on
P(X). Define
ρ (E)=ν (X)−ν (E′) for E⊂X. The measurable sets
Sν and Sρ and the set S={E⊂X/ν (E)=ρ (E)} are investigated in general, and in the
presence of regularity or modularity assumptions on ν. This is also done for
ν0(E)=inf{ν (M)/E⊂M∈Sν }. General properties of ν are derived when ν is
weakly submodular. Applications and numerous examples are given. |
| format | Article |
| id | doaj-art-be3c76d458cf4c6681ed0acc0bdbe99a |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-be3c76d458cf4c6681ed0acc0bdbe99a2025-08-20T02:18:35ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252003-01-012003846147410.1155/S0161171203208115On finitely subadditive outer measures and modularity propertiesCharles Traina0Department of Mathematics and Computer Science, St. John's University, 8000 Utopia Parkway, Jamaica 11439, NY, USALet ν be a finite, finitely subadditive outer measure on P(X). Define ρ (E)=ν (X)−ν (E′) for E⊂X. The measurable sets Sν and Sρ and the set S={E⊂X/ν (E)=ρ (E)} are investigated in general, and in the presence of regularity or modularity assumptions on ν. This is also done for ν0(E)=inf{ν (M)/E⊂M∈Sν }. General properties of ν are derived when ν is weakly submodular. Applications and numerous examples are given.http://dx.doi.org/10.1155/S0161171203208115 |
| spellingShingle | Charles Traina On finitely subadditive outer measures and modularity properties International Journal of Mathematics and Mathematical Sciences |
| title | On finitely subadditive outer measures and modularity properties |
| title_full | On finitely subadditive outer measures and modularity properties |
| title_fullStr | On finitely subadditive outer measures and modularity properties |
| title_full_unstemmed | On finitely subadditive outer measures and modularity properties |
| title_short | On finitely subadditive outer measures and modularity properties |
| title_sort | on finitely subadditive outer measures and modularity properties |
| url | http://dx.doi.org/10.1155/S0161171203208115 |
| work_keys_str_mv | AT charlestraina onfinitelysubadditiveoutermeasuresandmodularityproperties |