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 |
| Published: |
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 |
| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |