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Matematicheskaya Fizika, Analiz, Geometriya [Mathematical Physics, Analysis, Geometry], 2000, Volume 7, Number 1, Pages 35–48
(Mi jmag392)
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This article is cited in 5 scientific papers (total in 5 papers)
Point realization of Boolean actions of countable inductive limits of locally compact groups
Alexandre I. Danilenko Department of Mathematics and Mechanics, Kharkov National University, 4 Svobody Sq., Kharkov, 61077, Ukraine
Abstract:
Let $G$ be a CILLC-group, i.e., the inductive limit of an increasing sequence of its closed locally compact subgroups. Every nonsingular action of $G$ on a measure space $(X,\mathcal B,\mu)$ generates a continuous action of $G$ on the underlying Boolean $\sigma$-algebra $\mathcal M[\mu]=\mathcal B/I_\mu$, where $I_\mu$ is the ideal of $\mu$-null subsets. It is known that the converse is true for any locally compact $G$: every abstract Boolean $G$-space is associated with some Borel nonsingular action of $G$. In the present work this assertion is generalized to arbitrary CILLC-groups. In addition, we conctruct a free measure preserving action of $G$ on a standard probability space.
Citation:
Alexandre I. Danilenko, “Point realization of Boolean actions of countable inductive limits of locally compact groups”, Mat. Fiz. Anal. Geom., 7:1 (2000), 35–48
Linking options:
https://www.mathnet.ru/eng/jmag392 https://www.mathnet.ru/eng/jmag/v7/i1/p35
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Abstract page: | 135 | Full-text PDF : | 68 |
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