Negligible sets of Radon measures
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- by P. Prinz
- Proc. Amer. Math. Soc. 89 (1983), 440-444
- DOI: https://doi.org/10.1090/S0002-9939-1983-0715862-8
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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
- N. Bourbaki, Éléments de mathématique. Fasc. XIII. Livre VI: Intégration. Chapitres 1, 2, 3 et 4: Inégalités de convexité, Espaces de Riesz, Mesures sur les espaces localement compacts, Prolongement d’une mesure, Espaces $L^{p}$, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1175, Hermann, Paris, 1965 (French). Deuxième édition revue et augmentée. MR 0219684
- 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
Bibliographic 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