Applications of outer measures to separation properties of lattices and regular or σ‐smooth measures
Pao-Sheng Hsu · International Journal of Mathematics and Mathematical Sciences · 1994
Associated with a 0 − 1 measure μ ∈ I(ℒ) where ℒ is a lattice of subsets of X are outer measures μ′ and ; associated with a σ‐smooth 0 − 1 measure μ ∈ Iσ(ℒ) is an outer measure μ″ or with μ ∈ Iσ(ℒ′), ℒ′ being the complementary lattice, another outer measure . These outer measures and their associated measurable sets are used to establish separation properties on ℒ and regularity and σ‐smoothness of μ. Separation properties between two lattices ℒ1 and ℒ2, ℒ1⫅ℒ2, are similarly investigated. Notions of strongly σ‐smooth and slightly regular measures are also used.