Finitely subadditive outer measures, finitely superadditive inner measures and their measurable sets
نویسندگان
چکیده
منابع مشابه
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 ⊂ M ∈ Sν}. General properties of ν are derived when ν is weakly submodular. Applications and nu...
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Given a nonempty abstract set X, and a covering class C, and a finite, finitely subadditive outer measure ν, we construct an outer measure ν and investigate conditions for ν to be submodular. We then consider several other set functions associated with ν and obtain conditions for equality of these functions on the lattice generated by C. Lastly, we describe a construction of a finite, finitely ...
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The present paper is intended as a first step toward the establishment of a general theory of finitely subadditive outer measures. First, a general method for constructing a finitely subadditive outer measure and an associated finitely additive measure on any space is presented. This is followed by a discussion ofthe theory ofinner measures, their construction, and the relationship oftheir prop...
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Let L be a linear space of real bounded random variables on the probability space (Ω,A, P0). There is a finitely additive probability P on A, such that P ∼ P0 and EP (X) = 0 for all X ∈ L, if and only if c EQ(X) ≤ ess sup(−X), X ∈ L, for some constant c > 0 and (countably additive) probability Q on A such that Q ∼ P0. A necessary condition for such a P to exist is L − L+∞ ∩ L + ∞ = {0}, where t...
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 1996
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s016117129600066x