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 Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2009, Issue 3, Pages 114–127 (Mi vuu31)

MATHEMATICS

Some properties of the operator of the measure extension

A. G. Chentsov

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: The operator defining for a measure on algebra of sets, the extension on the sigma-algebra generated by the given algebra is considered. On the basis of the representation of the extended measure in the minimax terms, the property of the isometric isomorphism for the above-mentioned operator for the traditional normalizations is established. Some properties connected with the preservation of order relations under the given operator are established.

Keywords: algebra of sets, measure, extension of measure, isometric isomorphism.

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Document Type: Article
UDC: 517.987.1
MSC: 28A33

Citation: A. G. Chentsov, “Some properties of the operator of the measure extension”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2009, no. 3, 114–127

Citation in format AMSBIB
\Bibitem{Che09} \by A.~G.~Chentsov \paper Some properties of the operator of the measure extension \jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki \yr 2009 \issue 3 \pages 114--127 \mathnet{http://mi.mathnet.ru/vuu31}