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Mat. Sb., 2014, Volume 205, Number 2, Pages 39–70 (Mi msb8202)  

This article is cited in 9 scientific papers (total in 9 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

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


DOI: https://doi.org/10.4213/sm8202

Full text: PDF file (700 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2014, 205:2, 192–219

Bibliographic databases:

UDC: 517.938
MSC: 28D15, 37A15
Received: 21.12.2012 and 26.08.2013

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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. I. Bufetov, “Finiteness of ergodic unitarily invariant measures on spaces of infinite matrices”, Ann. Inst. Fourier, 64:3 (2014), 893–907  crossref  mathscinet  zmath  isi  elib  scopus
    2. A. I. Bufetov, “Infinite determinantal measures and the ergodic decomposition of infinite Pickrell measures. I. Construction of infinite determinantal measures”, Izv. Math., 79:6 (2015), 1111–1156  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. Proc. Steklov Inst. Math., 292 (2016), 94–111  mathnet  crossref  crossref  mathscinet  isi  elib
    4. A. I. Bufetov, “Infinite determinantal measures and the ergodic decomposition of infinite Pickrell measures. II. Convergence of infinite determinantal measures”, Izv. Math., 80:2 (2016), 299–315  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. A. I. Bufetov, “Infinite determinantal measures and the ergodic decomposition of infinite Pickrell measures. III. The infinite Bessel process as the limit of the radial parts of finite-dimensional projections of infinite Pickrell measures”, Izv. Math., 80:6 (2016), 1035–1056  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    6. Y. Qiu, “Ergodic measures on compact metric spaces for isometric actions by inductively compact groups”, Proc. Amer. Math. Soc., 145:4 (2017), 1593–1598  crossref  mathscinet  zmath  isi  scopus
    7. Y. Qiu, “Infinite random matrices & ergodic decomposition of finite and infinite Hua-Pickrell measures”, Adv. Math., 308 (2017), 1209–1268  crossref  mathscinet  zmath  isi  elib  scopus
    8. A. I. Bufetov, Y. Qiu, “Ergodic measures on spaces of infinite matrices over non-Archimedean locally compact fields”, Compos. Math., 153:12 (2017), 2482–2533  mathnet  crossref  mathscinet  zmath  isi  scopus
    9. Qiu Ya., “Ergodic Measures on Infinite Skew-Symmetric Matrices Over Non-Archimedean Local Fields”, Group. Geom. Dyn., 13:4 (2019), 1401–1416  crossref  mathscinet  zmath  isi
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