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A general measure decomposition theorem by means of the generalized wallman remainder

Part of: Classical measure theory

Published online by Cambridge University Press:  09 April 2009

George Bachman  and
Panagiotis D. Stratigos
George Bachman
Affiliation:
Department of Mathematics Polytechnic Institute of New YorkBrooklyn, New York 11201, U.S.A.
Panagiotis D. Stratigos
Affiliation:
Department of Mathematics Long Island UniversityBrooklyn, New York 11202, U.S.A.
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Abstract

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Let ℒ be a lattice of subsets of a set X. Let MR (ℒ) denote the set of all ℒ-regular (finitely additive) measures on the algebra generated by ℒ. Under the assumption that ℒ is disjunctive, in the first part of the paper, criteria are obtained for the σ-smoothness, τ-smoothness, and tightness of elements of MR(ℒ) in terms of the general Wallman remander. in the second part of the paper, various applications are given, and, in particular, extensions and refinements of the Yoside-Hewitt Decom position Theorem are obtained.

MSC classification

Secondary: 28A60: Measures on Boolean rings, measure algebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 36 , Issue 1 , February 1984 , pp. 87 - 105
Copyright
Copyright © Australian Mathematical Society 1984

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