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Measures on totally ordered spaces

Published online by Cambridge University Press:  26 February 2010

A. Sapounakis
Affiliation:
Department of Pure Mathematics, The University of Liverpool, Liverpool, 206 Church Street S.E., Minneapolis, Minnesota, 55455, U. S. A.
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Extract

The concept of uniform regularity of a measure on a compact space—a property which allows uniform approximation of the measure on all compact sets—was introduced and discussed in [1], [2] and [3]. Further some extensions of the notion of uniform regularity are given in [4] and [6].

Type
Research Article
Copyright
Copyright © University College London 1980

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References

1.Babiker, A. G. A. G.. “On uniformly regular topological measure spaces”. Duke Math. J., 43 (1976), 775789.Google Scholar
2.Babiker, A. G. A. G.. “Structural properties of uniformly regular measures on compact spaces”. Annales de la Societe Scientifique de Bruxelles, 90 (1976), 289297.Google Scholar
3.Babiker, A. G. A. G.. “Uniform regularity of measures on compact spaces”. J. reine. angew. Math., 289 (1977), 188198.Google Scholar
4.Babiker, A. G. A. G.. “Uniform regularity of measures on locally compact spaces”. J. reine angew. Math., 298 (1978), 6573.Google Scholar
5.Babiker, A. G. A. G.. “Lifting properties and uniform regularity of Lebesgue measures on topological spaces”. (Submitted for publication.)Google Scholar
6.Babiker, A. G. A. G. and Sapounakis, A.. “Some regularity conditions on topological measure spaces”. (Submitted for publication.)Google Scholar
7.Edgar, G. A.. “Measurable weak sections”. Illinois J. Math., 20 (1976), 630646.Google Scholar
8.Gillman, L. and Jerison, M.. Rings of continuous functions (Van Nostrand, N. Y., 1960).Google Scholar
9.Halmos, P. R.. Measure theory (Van Nostrand, N. Y., 1959).Google Scholar
10.Kelley, J. L.. General Topology (Van Nostrand, N. Y., 1955).Google Scholar
11.Kingman, J. F. and Taylor, S. J.. Introduction to measure and probability (Cambridge University Press, 1965).Google Scholar
12.Knowles, J. D.. “On the existence of non-atomic measures”. Mathematika, 14 (1967), 6267.Google Scholar
13.Knowles, J. D.. “Measures on topological spaces”. Proc. London Math. Soc., (1967) 139156.Google Scholar
14.Steen, L. A. and Seebach, S. A. jr. Counterexamples in topology (Springer-Verlag, New York, 1978).Google Scholar
15.Varadarajan, V. S.. “Measures on topological spaces”. Math. Sb. Ns., 55 (1961), 33100 (Russian). Amer. Math. Soc. Translations, Series 2, 48 (1961), 141-228 (English).Google Scholar