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Funktsional. Anal. i Prilozhen., 2018, Volume 52, Issue 4, Pages 23–37 (Mi faa3615)  

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

Combinatorial Invariants of Metric Filtrations and Automorphisms; the Universal Adic Graph

A. M. Vershikabc, P. B. Zatitskiida

a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
b St. Petersburg State University, Mathematics and Mechanics Faculty
c Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
d Saint Petersburg State University

Abstract: We suggest a combinatorial classification of metric filtrations of measure spaces; a complete invariant of such a filtration is its combinatorial scheme, a measure on the space of hierarchies of the group $\mathbb Z$. In turn, the notion of a combinatorial scheme is a source of new metric invariants of automorphisms approximated by means of basic filtrations. We construct a universal graph with an adic structure such that every automorphism can be realized on its path space.

Keywords: uniform approximation, filtrations, combinatorial definiteness, universal adic graph.

Funding Agency Grant Number
Russian Science Foundation 17-71-20153


DOI: https://doi.org/10.4213/faa3615

Full text: PDF file (236 kB)
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English version:
Functional Analysis and Its Applications, 2018, 52:4, 258–269

Bibliographic databases:

UDC: 519.1+519.2
Received: 18.09.2018

Citation: A. M. Vershik, P. B. Zatitskii, “Combinatorial Invariants of Metric Filtrations and Automorphisms; the Universal Adic Graph”, Funktsional. Anal. i Prilozhen., 52:4 (2018), 23–37; Funct. Anal. Appl., 52:4 (2018), 258–269

Citation in format AMSBIB
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\vol 52
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\pages 23--37
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\pages 258--269
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. M. Vershik, P. B. Zatitskii, “On a universal Borel adic space”, J. Math. Sci. (N. Y.), 240:5 (2019), 515–524  mathnet  crossref
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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