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The problem of describing central measures on the path spaces of graded graphs. / Vershik, A.M.
в: Functional Analysis and its Applications, № 4, 2014, стр. 256-271.Результаты исследований: Научные публикации в периодических изданиях › статья
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TY - JOUR
T1 - The problem of describing central measures on the path spaces of graded graphs
AU - Vershik, A.M.
PY - 2014
Y1 - 2014
N2 - © 2014, Springer Science+Business Media New York. 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.
AB - © 2014, Springer Science+Business Media New York. 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.
U2 - 10.1007/s10688-014-0069-5
DO - 10.1007/s10688-014-0069-5
M3 - Article
SP - 256
EP - 271
JO - Functional Analysis and its Applications
JF - Functional Analysis and its Applications
SN - 0016-2663
IS - 4
ER -
ID: 7061251