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Generic non-singular Poisson suspension is of type III1

Part of: Stochastic processes Ergodic theory

Published online by Cambridge University Press:  05 March 2021

ALEXANDRE I. DANILENKO Open the ORCID record for ALEXANDRE I. DANILENKO [Opens in a new window] ,
ZEMER KOSLOFF  and
EMMANUEL ROY
ALEXANDRE I. DANILENKO
Affiliation:
B. Verkin Institute for Low Temperature Physics & Engineering of Ukrainian National Academy of Sciences, 47 Lenin Ave., Kharkiv61164, Ukraine (e-mail: alexandre.danilenko@gmail.com)
ZEMER KOSLOFF*
Affiliation:
Einstein Institute of Mathematics, Hebrew University of Jerusalem, Givat Ram. Jerusalem9190401, Israel
EMMANUEL ROY
Affiliation:
Laboratoire Analyse, Géométrie et Applications, CNRS UMR 7539, Université Paris 13, Institut Galilée, 99 avenue Jean-Baptiste Clément, F-93430Villetaneuse, France (e-mail: roy@math.univ-paris13.fr)
*
e-mail: zemer.kosloff@mail.huji.ac.il
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Abstract

It is shown that for a dense $G_\delta $ -subset of the subgroup of non-singular transformations (of a standard infinite $\sigma $ -finite measure space) whose Poisson suspensions are non-singular, the corresponding Poisson suspensions are ergodic and of Krieger’s type III1.

Keywords

non-singular ergodic theoryPoisson suspensionorbit equivalence

MSC classification

Primary: 37A40: Nonsingular (and infinite-measure preserving) transformations 60G55: Point processes
Secondary: 37A50: Relations with probability theory and stochastic processes
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 42 , Issue 4 , April 2022 , pp. 1415 - 1445
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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