Characterizations of outer measures associated with lattice measures

Pao-Sheng Hsu

International Journal of Mathematics and Mathematical Sciences, 2000, vol. 24, 1-13

Abstract:

Let ν be a finite countably subadditive outer measure defined on all subsets of a set X , take a collection ℂ of subsets of X containing X and ∅ , we derive an outer measure ρ using ν on sets in ℂ . By applying this general framework on two special cases in which ν = μ ″ , one where μ ∈ M σ ( 𝔏 ) and the other where μ ∈ M σ ( 𝔏 1 ) , 𝔏 1 ⫅ 𝔏 2 being lattices on a set X , we obtain new characterizations of the outer measure μ ″ . These yield useful relationships between various set functions including μ i , μ j , μ ″ , and μ ′ .

Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:297464

DOI: 10.1155/S016117120000329X

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