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Ergodic measures and the definability of subgroups via normal extensions of such measures
A. B. Kharazishvili A. Razmadze Mathematical Institute,
University Street, 2, Tbilisi 0186, Georgia
Аннотация:
It is shown that any subgroup $H$ of an uncountable $\sigma$-compact locally compact topological group $\Gamma$ is completely determined by a certain family of left $H$-invariant extensions of the left Haar measure $\mu$ on $\Gamma$. An abstract analogue of this fact is also established for a nonzero $\sigma$-finite ergodic measure given on an uncountable commutative group.
Ключевые слова:
Locally compact topological group, Haar measure, invariant extension of measure, ergodicity, commutative group.
Образец цитирования:
A. B. Kharazishvili, “Ergodic measures and the definability of subgroups via normal extensions of such measures”, Theory Stoch. Process., 18(34):1 (2012), 58–64
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/thsp18 https://www.mathnet.ru/rus/thsp/v18/i1/p58
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