On Finitely Subadditive Outer Measures and Modularity Properties
نویسنده
چکیده
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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