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Applications of outer measures to separation properties of lattices and regular or σ -smooth measures

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  • Pao-Sheng Hsu

Abstract

Associated with a 0 − 1 measure μ ∈ I ( ℒ ) where ℒ is a lattice of subsets of X are outer measures μ ′ and μ ˜ ; associated with a σ -smooth 0 − 1 measure μ ∈ I σ ( ℒ ) is an outer measure μ ″ or with μ ∈ I σ ( ℒ ′ ) , ℒ ′ being the complementary lattice, another outer measure μ ˜ ˜ . 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 ℒ 1 and ℒ 2 , ℒ 1 ⫅ ℒ 2 , are similarly investigated. Notions of strongly σ -smooth and slightly regular measures are also used.

Suggested Citation

  • Pao-Sheng Hsu, 1996. "Applications of outer measures to separation properties of lattices and regular or σ -smooth measures," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 19, pages 1-10, January.
    • Handle: RePEc:hin:jijmms:364238
    DOI: 10.1155/S016117129600035X
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