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The product of pre-Radon measures

Published online by Cambridge University Press:  17 April 2009

Susumu Okada
Susumu Okada
Affiliation:
School of Mathematical Sciences, Flinders University of South Australia, Bedford Park, South Australia 5042, Australia.
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Abstract

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Let μ and ν be non-σ-finite pre-Radon measures on topological spaces X and Y respectively. Then there exists a unique pre-Radon measure λ on the product space X × Y which satisfies λ(A × B) = μ(A)ν(B) for all Borel sets A in X and B in Y such that μ(A) < ∞ and ν(B) < ∞.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 25 , Issue 2 , April 1982 , pp. 243 - 250
Copyright
Copyright © Australian Mathematical Society 1982

References

[1]Amemiya, Ichiro, Okada, Susumu and Okazaki, Yoshiaki, “Pre-Radon measures on topological spaces”, Kodai Math. J. 1 (1978), 101–132.CrossRefGoogle Scholar
[2]Bourbaki, N., Éléments de mathématique. Fasc. XXXV. Livre VI: Intégration. Chapitre IX: Intégration sur les espaaes topologiques séparés (Actualités Scientifiques et Industrielles, 1343. Hermann, Paris, 1969).Google Scholar
[3]Fremlin, D.H., Topological Riesz spaces and measure theory (Cambridge University Press, Cambridge, 1974).CrossRefGoogle Scholar
[4]Fremlin, D.H., “Quasi-Radon measure spaces”, unpublished manuscript.Google Scholar