This article is cited in 3 papers

Groups of homeomorphisms of the line. Criteria for the existence of invariant and projectively invariant measures in terms of the commutator subgroup

L. A. Beklaryan

Central Economics and Mathematics Institute, RAS, Moscow

Abstract: Existence criteria for invariant and projectively invariant measures are obtained for a group $G$ of homeomorphisms of the line. These criteria are formulated in terms of the commutator subgroup $[G,G]$. For the special (but very important) case of groups of homeomorphisms of the line containing a freely acting element we obtain a criterion for the existence of a projectively invariant measure in the form of the absence of a special subgroup with two generators in which one of the generating elements is a freely acting element.
Bibliography: 20 titles.

Keywords: groups of homeomorphisms of the line (the circle), invariant measure, projectively invariant measures.

UDC: 512.544.42

MSC: Primary 22F50, 37E05; Secondary 37A15

Received: 21.11.2013 and 03.10.2014

DOI: 10.4213/sm8306

 English version: Sbornik: Mathematics, 2014, 205:12, 1741–1760

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