On finitely subadditive outer measures and modularity properties

Charles Traina

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-14

Abstract:

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 S ν and S ρ 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 ν 0 ( E ) = inf { ν ( M ) / E ⊂ M ∈ S ν } . General properties of ν are derived when ν is weakly submodular. Applications and numerous examples are given.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:761252

DOI: 10.1155/S0161171203208115

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