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Zapiski Nauchnykh Seminarov POMI, 2018, Volume 468, Pages 24–38 (Mi znsl6598)  
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
Full-text PDF (264 kB) Citations (2)
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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
Received: 26.09.2018
English version:
Journal of Mathematical Sciences (New York), 2019, Volume 240, Issue 5, Pages 515–524
DOI: https://doi.org/10.1007/s10958-019-04369-9
Bibliographic databases:
Document Type: Article
UDC: 517.987
Language: Russian
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{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85068348744}
Linking options:
  • https://www.mathnet.ru/eng/znsl6598
  • https://www.mathnet.ru/eng/znsl/v468/p24
    • This publication is cited in the following 2 articles:
    1. A. M. Vershik, G. A. Veprev, P. B. Zatitskii, “Dynamics of metrics in measure spaces and scaling entropy”, Russian Math. Surveys, 78:3 (2023), 443–499  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. 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  mathscinet  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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