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Combinatorial invariants of metric filtrations and automorphisms; the universal adic graph. (English. Russian original) Zbl 1418.28001

Funct. Anal. Appl. 52, No. 4, 258-269 (2018); translation from Funkts. Anal. Prilozh. 52, No. 4, 23-37 (2018).
Summary: 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.

MSC:

28C15 Set functions and measures on topological spaces (regularity of measures, etc.)
05C90 Applications of graph theory
28D05 Measure-preserving transformations
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References:

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