Geodesic
The Problem of Describing Central Measures on the Path Spaces of Graded Graphs
Funkcionalʹnyj analiz i ego priloženiâ, Tome 48 (2014) no. 4, pp. 26-46

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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.
Keywords: invariant and central measures, projective limit of simplices, intrinsic metric, uniform compactness.
Mots-clés : filtrations 
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A. M. Vershik. The Problem of Describing Central Measures on the Path Spaces of Graded Graphs. Funkcionalʹnyj analiz i ego priloženiâ, Tome 48 (2014) no. 4, pp. 26-46. http://geodesic.mathdoc.fr/item/FAA_2014_48_4_a3/