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Sbornik: Mathematics, 1999, Volume 190, Issue 4, Pages 521–538
DOI: https://doi.org/10.1070/sm1999v190n04ABEH000391
(Mi sm391)
 

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

On the classification of groups of orientation-preserving homeomorphisms of $\mathbb R$. III. $\omega$-projectively invariant measures

L. A. Beklaryan

Central Economics and Mathematics Institute, RAS
References:
Abstract: General groups of orientation-preserving homeomorphisms of $\mathbb R$ are investigated. A series of metric invariants are defined for such groups: $\omega$-projectively invariant measures, where $\omega$ is a cardinal number. A theorem on the existence of an $\omega$-projectively invariant measure is formulated, which is a natural generalization of the Bogolyubov–Krylov theorem on the existence of an invariant measure for a circle homeomorphism. For groups with an $\omega$-projectively invariant measure “obstructions” to the existence of a 1-projectively invariant measure are analysed. The approach is based on the study of the topological structure of the set of all fixed points of the elements of the group, the orbits of points in the line, minimal sets, and the combinatorial properties of groups.
Received: 07.05.1998
Russian version:
Matematicheskii Sbornik, 1999, Volume 190, Number 4, Pages 43–62
DOI: https://doi.org/10.4213/sm391
Bibliographic databases:
UDC: 515.168.3
MSC: Primary 54H15, 58F11; Secondary 28D05, 20F38
Language: English
Original paper language: Russian
Citation: L. A. Beklaryan, “On the classification of groups of orientation-preserving homeomorphisms of $\mathbb R$. III. $\omega$-projectively invariant measures”, Mat. Sb., 190:4 (1999), 43–62; Sb. Math., 190:4 (1999), 521–538
Citation in format AMSBIB
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  • https://doi.org/10.1070/sm1999v190n04ABEH000391
  • https://www.mathnet.ru/eng/sm/v190/i4/p43
  • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник - 1992–2005 Sbornik: Mathematics
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    English version PDF:16
    References:78
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