International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 4, Pages 237-249
doi:10.1155/S016117120000329X

Characterizations of outer measures associated with lattice measures

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∈Mσ(𝔏) and the other where μ∈Mσ(𝔏1),𝔏1⫅𝔏2 being lattices on a set X, we obtain new characterizations of the outer measure μ″. These yield useful relationships between various set functions including μi,μj,μ″, and μ′.