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Demonstratio Mathematica

Editor-in-Chief: Vetro, Calogero

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Volume 51, Issue 1


On existence of the support of a Borel measure

Piotr A. Kozarzewski
  • Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, ul. Banacha 2, 02-097, Warsaw, Poland
  • Faculty of Cybernetics, Military University of Technology, ul. Gen. Witolda Urbanowicza 2, 00-908, Warsaw, Poland
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Published Online: 2018-05-30 | DOI: https://doi.org/10.1515/dema-2018-0010


We present arguments showing that the standard notion of the support of a probabilistic Borel measure is not well defined in every topological space. Our goal is to create a “very inseparable” space and to show the existence of a family of closed sets such that each of them is of full measure, but their intersection is empty. The presented classic construction is credited to Jean Dieudonné and dates back to 1939. We also propose certain, up to our best knowledge, new simplifications.

Keywords: set theory; ordinal numbers; measure

MSC 2010: Primary: 28E15; Secondary: 03E10; 28A05


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About the article

Received: 2017-11-22

Accepted: 2018-04-12

Published Online: 2018-05-30

Citation Information: Demonstratio Mathematica, Volume 51, Issue 1, Pages 76–84, ISSN (Online) 2391-4661, DOI: https://doi.org/10.1515/dema-2018-0010.

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© 2018 Piotr A. Kozarzewski. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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