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Some Constructions in Abstract Measure Theory

Published online by Cambridge University Press:  20 November 2018

D. J. Lutzer
D. J. Lutzer*
Affiliation:
University of Pittsburgh, Pittsburgh, Pennsylvania
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In this paper we construct two examples which elucidate the relationships between several σ-algebras that arise in measure-theoretic constructions on locally compact spaces and groups. For any space X let (X) be the Borelσ-algebra on X, i.e., the smallest σ-algebra of subsets of X which contains the family of all closed subsets of X. Let δ (X) be the smallest δ-ring of subsets of X which contains every compact subset of X, where by a δ-ring we mean a collection of subsets of X which is closed under the formation of countable intersections, finite unions and relative complements. Let σ(X) be the smallest σ-ring of subsets of X which contains all compact subsets of X, where by a σ-ring we mean a collection of subsets of X which is closed under the formation of countable unions, finite intersections and relative complements.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 4 , 01 August 1975 , pp. 860 - 866
Copyright
Copyright © Canadian Mathematical Society 1975

References

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