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 Mat. Sb., 1996, Volume 187, Number 6, Pages 73–84 (Mi msb137)

The group of diffeomorphisms of the half-line, and random Cantor sets

Yu. A. Neretin

Moscow State Institute of Electronics and Mathematics

Abstract: A certain one-parameter family of measures is constructed on the space of closed totally disconnected subsets of the half-line without isolated points. It is shown that these measures are quasi-invariant with respect to the group of smooth diffeomorphisms of the half-line, and the Radon–Nikodym derivatives are explicitly computed.

DOI: https://doi.org/10.4213/sm137

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English version:
Sbornik: Mathematics, 1996, 187:6, 857–868

Bibliographic databases:

UDC: 517.98
MSC: Primary 58D05, 60D05; Secondary 20C99, 22E65, 22E67, 28C10, 81R10

Citation: Yu. A. Neretin, “The group of diffeomorphisms of the half-line, and random Cantor sets”, Mat. Sb., 187:6 (1996), 73–84; Sb. Math., 187:6 (1996), 857–868

Citation in format AMSBIB
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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. Tatsuuma, N, “On group topologies and unitary representations of inductive limits of topological groups and the case of the group of diffeomorphisms”, Journal of Mathematics of Kyoto University, 38:3 (1998), 551
2. Hirai T., “Group topologies and unitary representations of the group of diffeomorphisms”, Analysis on Infinite-Dimensional Lie Groups and Algebras, 1998, 145–153
3. Goldin G.A., Moschella U., Sakuraba T., “Measures on spaces of infinite-dimensional configurations, group representations, and statistical physics”, Lie Theory and Its Applications in Physics V, Proceedings, 2004, 313–326
4. Gnedin, A, “Regenerative composition structures”, Annals of Probability, 33:2 (2005), 445
5. Gnedin, A, “Asymptotic laws for compositions derived from transformed subordinators”, Annals of Probability, 34:2 (2006), 468
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