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Sbornik: Mathematics, 2014, Volume 205, Issue 2, Pages 192–219
DOI: https://doi.org/10.1070/SM2014v205n02ABEH004371 (Mi sm8202) 		 
This article is cited in 17 scientific papers (total in 17 papers)

Ergodic decomposition for measures quasi-invariant under a Borel action of an inductively compact group

A. I. Bufetovabcde

a Steklov Mathematical Institute of the Russian Academy of Sciences
b Rice University
c A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow
d National Research University "Higher School of Economics"
e Aix-Marseille Université
English version PDF (619 kB) Citations (17)
References:
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DOI: https://doi.org/10.1070/SM2014v205n02ABEH004371
Abstract: The aim of this paper is to prove ergodic decomposition theorems for probability measures which are quasi-invariant under Borel actions of inductively compact groups as well as for $\sigma$-finite invariant measures. For infinite measures the ergodic decomposition is not unique, but the measure class of the decomposing measure on the space of projective measures is uniquely defined by the initial invariant measure.
Bibliography: 21 titles.
Keywords: ergodic decomposition, infinite-dimensional groups, quasi-invariant measure, infinite-dimensional unitary group, measurable decomposition.
Funding agency Grant number
Agence Nationale de la Recherche ANR-11-IDEX-0001-02
Alfred P. Sloan Foundation
Dynasty Foundation
Independent University of Moscow
Ministry of Education and Science of the Russian Federation MK-6734.2012.1
МД-2859.2014.1
Russian Academy of Sciences - Federal Agency for Scientific Organizations
Russian Foundation for Basic Research 10-01-93115-NTsNIL
11-01-00654
12-01-31284
12-01-33020
13-01-12449
Received: 21.12.2012 and 26.08.2013
Russian version:
Matematicheskii Sbornik, 2014, Volume 205, Number 2, Pages 39–70
DOI: https://doi.org/10.4213/sm8202
Bibliographic databases:
Document Type: Article
UDC: 517.938
MSC: 28D15, 37A15
Language: English
Original paper language: Russian
Citation: A. I. Bufetov, “Ergodic decomposition for measures quasi-invariant under a Borel action of an inductively compact group”, Mat. Sb., 205:2 (2014), 39–70; Sb. Math., 205:2 (2014), 192–219
Citation in format AMSBIB
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    • This publication is cited in the following 17 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:718
    Russian version PDF:315
    English version PDF:21
    References:113
    First page:94
     
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