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Zapiski Nauchnykh Seminarov POMI, 2018, Volume 468, Pages 24–38
(Mi znsl6598)
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This article is cited in 2 scientific papers (total in 2 papers)
I
On a universal Borel adic space
A. M. Vershikab, P. B. Zatitskiiba a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
b St. Petersburg State University, St. Petersburg, Russia
Abstract:
We prove that the so-called uniadic graph and its adic automorphism are Borel universal, i.e., every aperiodic Borel automorphism is isomorphic to the restriction of this automorphism to a subset invariant under the adic transformation, the isomorphism being defined on a universal (with respect to the measure) set. We develop the concept of basic filtrations and combinatorial definiteness of automorphisms suggested in our previous paper.
Key words and phrases:
filtration, finite definiteness, universality, uniadic graph, central measures.
Received: 26.09.2018
Citation:
A. M. Vershik, P. B. Zatitskii, “On a universal Borel adic space”, Representation theory, dynamical systems, combinatorial methods. Part XXIX, Zap. Nauchn. Sem. POMI, 468, POMI, St. Petersburg, 2018, 24–38; J. Math. Sci. (N. Y.), 240:5 (2019), 515–524
Linking options:
https://www.mathnet.ru/eng/znsl6598 https://www.mathnet.ru/eng/znsl/v468/p24
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Abstract page: | 217 | Full-text PDF : | 40 | References: | 35 |
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