Generic non-singular Poisson suspension is of type III1

Alexandre I. Danilenko; Zemer Kosloff; Emmanuel Roy

doi:10.1017/etds.2021.5

Generic non-singular Poisson suspension is of type III₁

Alexandre I. Danilenko, Zemer Kosloff, Emmanuel Roy

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

It is shown that for a dense Gδ-subset of the subgroup of non-singular transformations (of a standard infinite σ-finite measure space) whose Poisson suspensions are non-singular, the corresponding Poisson suspensions are ergodic and of Krieger's type III1.

Original language	English
Pages (from-to)	1415-1445
Number of pages	31
Journal	Ergodic Theory and Dynamical Systems
Volume	42
Issue number	4
DOIs	https://doi.org/10.1017/etds.2021.5
State	Published - 5 Apr 2022

Bibliographical note

Publisher Copyright:
© 2021 The Author(s).

Keywords

Poisson suspension
non-singular ergodic theory
orbit equivalence

Access to Document

10.1017/etds.2021.5

Cite this

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AB - It is shown that for a dense Gδ-subset of the subgroup of non-singular transformations (of a standard infinite σ-finite measure space) whose Poisson suspensions are non-singular, the corresponding Poisson suspensions are ergodic and of Krieger's type III1.

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KW - orbit equivalence

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