Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-23T05:34:30.413Z Has data issue: false hasContentIssue false
  • English
  • Français

Functions and measures on products spaces

Part of: Classical measure theory

Published online by Cambridge University Press:  26 February 2010

A. G. Babiker  and
J. D. Knowles
A. G. Babiker
Affiliation:
School of Mathematical Sciences, University of Khartoum, P.O. Box 321, Khartoum, Sudan.
J. D. Knowles
Affiliation:
Westfield College, London.
Get access

Extract

The results we present were motivated by the product measure problem for Baire measures. For two completely regular Hausdorff spaces X and Y, with totally finite a- additive measures μ and ν defined on the Baire σ- algebras ℬ0(X) and ℬ0(Y) respectively, under what conditions may we define a measure λ on the Baire σ-algebra ℬ0(X × Y), extending the product measure μ ⊗ ν defined on the product σ-algebra ℬ0(X) × ℬ0(Y) and satisfying a Fubini theorem?

MSC classification

Secondary: 28A35: Measures and integrals in product spaces
Type
Research Article
Information
Mathematika , Volume 32 , Issue 1 , June 1985 , pp. 60 - 67
Copyright
Copyright © University College London 1985

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Bledsoe, W. W. and Morse, A. P.. Product Measures. Trans. Amer. Math. Soc., 79 (1955), 173–215.Google Scholar
2.Bourbaki, N.. General Topology (Addison Wesley, 1966).Google Scholar
3.Bourbaki, N.. Integration, Ch. IX (Hermann, Paris, 1969).Google Scholar
4.Comfort, W. W. and Hager, A. W.. The projection mapping and other continuous functions on a product space. Math. Scand., 28 (1971), 77–90.CrossRefGoogle Scholar
5.Fremlin, D. H.. Products of radon measures: a counter-example. Canad. Math. Bull., 19 (1976), 285–289.Google Scholar
6.Fremlin, D. H., Garling, D. J. H. and Haydon, R. G.. Bounded measures on topological spaces. Proc. London Math. Soc., 25 (1972), 115–136.CrossRefGoogle Scholar
7.Gillman, L. and Jerison, M.. Rings of continuous functions (Van Nostrand, 1960).CrossRefGoogle Scholar
8.Gowrisankaran, K.. Measurability of functions in product spaces. Proc. Amer. Math. Soc., 31 (1972), 485–488.CrossRefGoogle Scholar
9.Knowles, J. D.. Measures on topological spaces. Proc. London Math. Soc., 17 (1967), 139–156.CrossRefGoogle Scholar
10.Rao, B. V.. On discrete Borel spaces. Acta Math. Acad. Sci. Hungaricae, 22 (1971), 197–198.Google Scholar
11.Ressel, P.. Some continuity and measurability results on spaces of measures. Math. Scand., 40 (1977), 69–78.Google Scholar
12.Ross, K. A. and Stromberg, K.. Baire sets and Baire measures. Arkiv för Mat., 6 (1965), 151–160.Google Scholar
13.Sentilles, F. D.. Bounded continuous functions on a completely regular space. Trans. Amer. Math. Soc., 168 (1972), 311–336.CrossRefGoogle Scholar
14.Weinsacker, H.. Strong measurability, lifting and the Choquet theorem. Springer Lecture Notes 695, Measure theory applications to stochastic analysis Proc. (1977). Ed. Kallianpur, G. and Kolzow, D. 1978.Google Scholar
15.Varadarajan, V. S.. Measures on topological spaces. Mat. Sb., NS. 55 (97) (1961), 33–100 (Russian)–Amer. Math. Soc Transl. (2), 48, 141–228 (English).Google Scholar