On existence of the support of a Borel measure

On existence of the support of a Borel measure AbstractWe 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

On existence of the support of a Borel measure

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Publisher
De Gruyter Open
Copyright
© 2018 Piotr A. Kozarzewski
ISSN
0420-1213
eISSN
2391-4661
D.O.I.
10.1515/dema-2018-0010
Publisher site
See Article on Publisher Site

Abstract

AbstractWe 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.

Journal

Demonstratio Mathematicade Gruyter

Published: May 30, 2018

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