Remarks on μ ″ -measurbale sets: regularity, σ -smootheness, and measurability

Carman Vlad

International Journal of Mathematics and Mathematical Sciences, 1999, vol. 22, 1-10

Abstract:

Let X be an arbitrary nonempty set and ℒ a lattice of subsets of X such that ϕ , X ∈ ℒ . 𝒜 ( ℒ ) is the algebra generated by ℒ and ℳ ( ℒ ) denotes those nonnegative, finite, finitely additive measures μ on 𝒜 ( ℒ ) . I ( ℒ ) denotes the subset of ℳ ( ℒ ) of nontrivial zero-one valued measures. Associated with μ ∈ I ( ℒ ) (or I σ ( ℒ ) ) are the outer measures μ ′ and μ ″ considered in detail. In addition, measurability conditions and regularity conditions are investigated and specific characteristics are given for 𝒮 μ ″ , the set of μ ″ -measurable sets. Notions of strongly σ -smooth and vaguely regular measures are also discussed. Relationships between regularity, σ -smoothness and measurability are investigated for zero-one valued measures and certain results are extended to the case of a pair of lattices ℒ 1 , ℒ 2 where ℒ 1 ⊂ ℒ 2 .

Date: 1999
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:872748

DOI: 10.1155/S0161171299223915

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