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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Negligible sets of Radon measures
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by P. Prinz PDF
Proc. Amer. Math. Soc. 89 (1983), 440-444 Request permission

Abstract:

Let $m$ be a Radon measure on a Hausdorff topological space $X$. Corresponding to three kinds of outer measures, three kinds of $m$-negligible sets are considered. The main theorem states that in a metacompact space $X$ each locally $m$-negligible set is $m$-negligible.
References
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  • Jean Dieudonné, Un exemple d’espace normal non susceptible d’une structure uniforme d’espace complet, C. R. Acad. Sci. Paris 209 (1939), 145–147 (French). MR 175
  • R. J. Gardner, The regularity of Borel measures and Borel measure-compactness, Proc. London Math. Soc. (3) 30 (1975), 95–113. MR 367145, DOI 10.1112/plms/s3-30.1.95
  • Roy A. Johnson, Another Borel measure-compact space which is not weakly Borel measure-complete, J. London Math. Soc. (2) 21 (1980), no. 2, 263–264. MR 575383, DOI 10.1112/jlms/s2-21.2.263
  • Laurent Schwartz, Radon measures on arbitrary topological spaces and cylindrical measures, Tata Institute of Fundamental Research Studies in Mathematics, No. 6, Published for the Tata Institute of Fundamental Research, Bombay by Oxford University Press, London, 1973. MR 0426084
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 89 (1983), 440-444
  • MSC: Primary 28C15
  • DOI: https://doi.org/10.1090/S0002-9939-1983-0715862-8
  • MathSciNet review: 715862