Infinitely fine partitions of measures spaces

Автор: Troitsky Vladimir Georgievich

Журнал: Владикавказский математический журнал @vmj-ru

Статья в выпуске: 3 т.1, 1999 года.

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In any measurable space one can find a hyperfinite infinitesimal partition, that is, a hyperfinite set of disjoint inner (in the sense of nonstandard analysis) measurable subsets such that every standard measurable set is representable as a union of sets of this collection. In this paper we characterize the various properties of measures in terms of infinitesimal partitions. In particular, we characterize the non-atomicness of the measures and give a short proof of the Sobchik-Hammer theorem.

Короткий адрес: https://sciup.org/14318586

IDR: 14318586

Список литературы Infinitely fine partitions of measures spaces

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