Geodesic
Criteria for the Existence of an Invariant Measure for Groups of Homeomorphisms of the Line
Matematičeskie zametki, Tome 95 (2014) no. 3, pp. 335-339.

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In [1] (1975), for finitely generated groups of homeomorphisms of the line (the circle), Plante obtained a criterion for the existence of an invariant measure. In the paper, we obtain a criterion for the existence of an invariant measure for groups of homeomorphisms of the line (the circle) such that every finitely generated subgroup of the group satisfies the Plante conditions.
Keywords: invariant measure, group of homeomorphisms, finitely generated subgroup
Mots-clés : Plante conditions. 
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L. A. Beklaryan. Criteria for the Existence of an Invariant Measure for Groups of Homeomorphisms of the Line. Matematičeskie zametki, Tome 95 (2014) no. 3, pp. 335-339. http://geodesic.mathdoc.fr/item/MZM_2014_95_3_a1/

[1] J. F. Plante, “Foliations with measure preserving holonomy”, Ann. of Math. (2), 102:2 (1975), 327–361 | DOI | MR | Zbl

[2] L. A. Beklaryan, “Invariantnye i proektivno invariantnye mery dlya grupp gomeomorfizmov $\mathbb R$, sokhranyayuschikh orientatsiyu”, Dokl. RAN, 332:6 (1993), 679–681 | MR | Zbl

[3] L. A. Beklaryan, “K voprosu o klassifikatsii grupp gomeomorfizmov $\mathbb R$, sokhranyayuschikh orientatsiyu. III. $\omega$-proektivno-invariantnye mery”, Matem. sb., 190:4 (1999), 43–62 | DOI | MR | Zbl

[4] L. A. Beklaryan, “K voprosu o klassifikatsii grupp gomeomorfizmov $\mathbb R$, sokhranyayuschikh orientatsiyu. II. Proektivno-invariantnye mery”, Matem. sb., 187:4 (1996), 3–28 | DOI | MR | Zbl