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Zap. Nauchn. Sem. POMI, 2018, Volume 468, Pages 24–38 (Mi znsl6598)  

This article is cited in 1 scientific paper (total in 1 paper)

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.

Funding Agency Grant Number
Russian Academy of Sciences - Federal Agency for Scientific Organizations PRAS-18-01


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English version:
Journal of Mathematical Sciences (New York), 2019, 240:5, 515–524

UDC: 517.987
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

Citation in format AMSBIB
\Bibitem{VerZat18}
\by A.~M.~Vershik, P.~B.~Zatitskii
\paper On a~universal Borel adic space
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XXIX
\serial Zap. Nauchn. Sem. POMI
\yr 2018
\vol 468
\pages 24--38
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6598}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2019
\vol 240
\issue 5
\pages 515--524
\crossref{https://doi.org/10.1007/s10958-019-04369-9}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85068348744}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. M. Vershik, P. B. Zatitskii, “Combinatorial Invariants of Metric Filtrations and Automorphisms; the Universal Adic Graph”, Funct. Anal. Appl., 52:4 (2018), 258–269  mathnet  crossref  crossref  isi  elib
  • Записки научных семинаров ПОМИ
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