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Generic non-singular Poisson suspension is of type III1

Published online by Cambridge University Press:  05 March 2021

ALEXANDRE I. DANILENKO
Affiliation:
B. Verkin Institute for Low Temperature Physics & Engineering of Ukrainian National Academy of Sciences, 47 Lenin Ave., Kharkiv 61164, Ukraine (e-mail: alexandre.danilenko@gmail.com)
ZEMER KOSLOFF
Affiliation:
Einstein Institute of Mathematics, Hebrew University of Jerusalem, Givat Ram. Jerusalem 9190401, Israel
EMMANUEL ROY
Affiliation:
Laboratoire Analyse, Géométrie et Applications, CNRS UMR 7539, Université Paris 13, Institut Galilée, 99 avenue Jean-Baptiste Clément, F-93430 Villetaneuse, France (e-mail: roy@math.univ-paris13.fr)

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.

Type
Original Article
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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