On existence of the support of a Borel measure

• Autorzy: Kozarzewski P. A.

Identyfikatory

DOI

10.1515/dema-2018-0010

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

set theory; ordinal numbers; measure

PL

teoria zbiorów; liczby porządkowe; miara

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2018
• Tom: Vol. 51, nr 1
• Strony: 76--84
• Opis fizyczny: Bibliogr. 18 poz.

Twórcy

autor

Kozarzewski P. A.

• 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

Bibliografia

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• [17] Moschovakis Y., Notes on Set Theory, Springer Science and Business Media, 2006
• [18] Hrbacek K., Jech T., Introduction to Set Theory, Third Edition, Revised and Expanded, CRC Press, 1999

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).