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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| Language: | English |
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Hindawi Limited
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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doaj-be3c76d458cf4c6681ed0acc0bdbe99a2020-11-24T23:55:22ZengHindawi LimitedInternational 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 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Charles Traina |
| spellingShingle |
Charles Traina On finitely subadditive outer measures and modularity properties International Journal of Mathematics and Mathematical Sciences |
| author_facet |
Charles Traina |
| author_sort |
Charles Traina |
| title |
On finitely subadditive outer measures and modularity properties |
| title_short |
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_sort |
on finitely subadditive outer measures and modularity properties |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2003-01-01 |
| 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. |
| url |
http://dx.doi.org/10.1155/S0161171203208115 |
| work_keys_str_mv |
AT charlestraina onfinitelysubadditiveoutermeasuresandmodularityproperties |
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