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Functional Analysis and Its Applications

, Volume 52, Issue 4, pp 258–269 | Cite as

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

  • A. M. VershikEmail author
  • P. B. Zatitskiy
Article
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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 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.

Key words

uniform approximation filtrations combinatorial definiteness universal adic graph 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.St. Petersburg Department of Steklov Institute of MathematicsSt. PetersburgRussia
  2. 2.St. Petersburg State UniversitySt. PetersburgRussia
  3. 3.Institute for Information Transmission ProblemsMoscowRussia

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