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Outer measures associated with lattice measures and their application

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  • Charles Traina

Abstract

Consider a set X and a lattice ℒ of subsets of X such that ϕ , X ∈ ℒ . M ( ℒ ) denotes those bounded finitely additive measures on A ( ℒ ) which are studied, and I ( ℒ ) denotes those elements of M ( ℒ ) which are 0 − 1 valued. Associated with a μ ∈ M ( ℒ ) or a μ ∈ M σ ( ℒ ) (the elements of M ( ℒ ) which are σ -smooth on ℒ ) are outer measures μ ′ and μ ″ . In terms of these outer measures various regularity properties of μ can be introduced, and the interplay between regularity, smoothness, and measurability is investigated for both the 0 − 1 valued case and the more general case. Certain results for the special case carry over readily to the more general case or with at most a regularity assumption on μ ′ or μ ″ , while others do not. Also, in the special case of 0 − 1 valued measures more refined notions of regularity can be introduced which have no immediate analogues in the general case.

Suggested Citation

  • Charles Traina, 1995. "Outer measures associated with lattice measures and their application," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 18, pages 1-10, January.
    • Handle: RePEc:hin:jijmms:834781
    DOI: 10.1155/S0161171295000937
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