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The problem of describing central measures on the path spaces of graded graphs. (English. Russian original) Zbl 1370.37005

Funct. Anal. Appl. 48, No. 4, 256-271 (2014); translation from Funkts. Anal. Prilozh. 48, No. 4, 26-46 (2014).
Summary: We suggest a new method for describing invariant measures on Markov compacta and on path spaces of graphs and, thereby, for describing characters of certain groups and traces of AF-algebras. The method relies on properties of filtrations associated with a graph and, in particular, on the notion of a standard filtration. The main tool is an intrinsic metric introduced on simplices of measures; this is an iterated Kantorovich metric, and the central result is that the relative compactness in this metric guarantees the possibility of a constructive enumeration of ergodic invariant measures. Applications include a number of classical theorems on invariant measures.

MSC:

37A05 Dynamical aspects of measure-preserving transformations
28D05 Measure-preserving transformations
46A55 Convex sets in topological linear spaces; Choquet theory
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References:

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