Geodesic
Combinatorial Invariants of Metric Filtrations and Automorphisms; the Universal Adic Graph
Funkcionalʹnyj analiz i ego priloženiâ, Tome 52 (2018) no. 4, pp. 23-37

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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, combinatorial definiteness, universal adic graph.
Mots-clés : filtrations 
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     author = {A. M. Vershik and P. B. Zatitskii},
     title = {Combinatorial {Invariants} of {Metric} {Filtrations} and {Automorphisms;} the {Universal} {Adic} {Graph}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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A. M. Vershik; P. B. Zatitskii. Combinatorial Invariants of Metric Filtrations and Automorphisms; the Universal Adic Graph. Funkcionalʹnyj analiz i ego priloženiâ, Tome 52 (2018) no. 4, pp. 23-37. http://geodesic.mathdoc.fr/item/FAA_2018_52_4_a1/