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Lifting properties and uniform regularity of lebesgue measures on topological spaces

Part of: Classical measure theory

Published online by Cambridge University Press:  26 February 2010

A. G. A. G. Babiker
A. G. A. G. Babiker
Affiliation:
School of Mathematical Sciences, University of Khartoum, P.O. Box 321, Khartoum, Sudan.
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Extract

Let (X, ℱ, μ) be a topological measure space with X a completely regular Hausdorff space and ℱ the σ-algebra of all μ-measurable sets, containing all the Baire sets of X. Consider the following two conditions on (X, ℱ, μ).

MSC classification

Secondary: 28A51: Lifting theory
Type
Research Article
Information
Mathematika , Volume 28 , Issue 2 , December 1981 , pp. 198 - 205
Copyright
Copyright © University College London 1981

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References

1.Babiker, A. G. A. G.. “On uniformly regular topological measure spaces”, Duke math. J., 43 (1976), 775–789.CrossRefGoogle Scholar
2.Babiker, A. G. A. G.. “Uniform regularity of measures on compact spaces”, J. reine angew. Math., 289 (1977), 188–198.Google Scholar
3.Babiker, A. G. A. G.. “Lebesgue measures on topological spaces”, Mathematika, 24 (1977), 52–59.CrossRefGoogle Scholar
4.Bourbaki, N.. Éléments de Mathematique, Integration, Chap. 1–5 (Paris, 1956).Google Scholar
5.Fremlin, D.. “On two theorems of Mokobodzki”, privately circulated from Math, dept., University of Essex, Colchester, England.Google Scholar
6.Gillman, L. and Jerison, M.. Rings of Continuous Functions (New York, 1960).CrossRefGoogle Scholar
7.Graf, S.. “On the existence of strong liftings in second countable topological spaces”, Pacific J. Math., 58 (1975), 419–426.CrossRefGoogle Scholar
8.Halmos, P. R.. Measure Theory (New York, 1955).Google Scholar
9.A., and Tulcea, C. Lonescu. Topics in the Theory of Liftings (Berlin-Heidelberg-New York, 1969).Google Scholar
10.Kelly, J.. General Topology (New York, 1955).Google Scholar
11.Knowles, J. D.. “Measures on topological spaces”, Proc. London Math. Soc, 17 (1967), 139–156.CrossRefGoogle Scholar
12.Losert, V.. “A measure space without the strong lifting property”, Math. Ann., 239 (1979), 119–128.CrossRefGoogle Scholar
13.Rochlin, V. A.. “On the fundamental ideas of measure theory”, Math. sb. (N.S.), 25 (67) (1949), 107–150 (Russian). A.M.S. translation, 71 (1952) (English).Google Scholar
14.Schwartz, L.. Radon Measures on Arbitrary Topological Spaces and Cylindrical Measures (Tata inst. and Oxford U.P., 1973).Google Scholar
15.Varadarajan, V. S.. “Measures on topological spaces”, Math. sb. (N.S.), 55 (97) (1961), 33–100 (Russian). A.M.S. translation, 48, 14-228 (English).Google Scholar