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Funktsional'nyi Analiz i ego Prilozheniya, 2014, Volume 48, Issue 4, Pages 26–46
DOI: https://doi.org/10.4213/faa3166 (Mi faa3166) 		 
This article is cited in 23 scientific papers (total in 24 papers)

The Problem of Describing Central Measures on the Path Spaces of Graded Graphs

A. M. Vershikabc

a Saint Petersburg State University
b St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
c Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
Full-text PDF (433 kB) Citations (24)
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DOI: https://doi.org/10.4213/faa3166
Abstract: 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, filtrations, intrinsic metric, uniform compactness.
Funding agency Grant number
Russian Science Foundation 14-11-00581
Received: 08.08.2014
English version:
Functional Analysis and Its Applications, 2014, Volume 48, Issue 4, Pages 256–271
DOI: https://doi.org/10.1007/s10688-014-0069-5
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: A. M. Vershik, “The Problem of Describing Central Measures on the Path Spaces of Graded Graphs”, Funktsional. Anal. i Prilozhen., 48:4 (2014), 26–46; Funct. Anal. Appl., 48:4 (2014), 256–271
Citation in format AMSBIB
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    • This publication is cited in the following 24 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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