Generic non-singular Poisson suspension is of type III1

Alexandre I. Danilenko; Zemer Kosloff; Emmanuel Roy

doi:https://doi.org/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

The Hebrew University of Jerusalem

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

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

Keywords

Poisson suspension
non-singular ergodic theory
orbit equivalence

All Science Journal Classification (ASJC) codes

Applied Mathematics
General Mathematics

Access to Document

https://doi.org/10.1017/etds.2021.5

Cite this

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title = "Generic non-singular Poisson suspension is of type III1",

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.",

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AU - Kosloff, Zemer

AU - Roy, Emmanuel

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N2 - 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.

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 - non-singular ergodic theory

KW - orbit equivalence

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M3 - مقالة

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EP - 1445

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

IS - 4

ER -