Combinatorial Invariants of Metric Filtrations and Automorphisms; the Universal Adic Graph
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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 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 wordsuniform approximation filtrations combinatorial definiteness universal adic graph
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