KRIEGER’S TYPE OF NONSINGULAR POISSON SUSPENSIONS AND IDPFT SYSTEMS

Alexandre I. Danilenko; Zemer Kosloff

doi:10.1090/proc/15695

KRIEGER’S TYPE OF NONSINGULAR POISSON SUSPENSIONS AND IDPFT SYSTEMS

Alexandre I. Danilenko
, Zemer Kosloff

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

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

Abstract

Given an infinite countable discrete amenable group Γ, we construct explicitly sharply weak mixing nonsingular Poisson Γ-actions of each Krieger’s type: III_λ, for λ ∈ [0, 1], and II_∞. The result is new even for Γ = Z. As these Poisson suspension actions are over very special dissipative base, we obtain also new examples of sharply weak mixing nonsingular Bernoulli Γ-actions and infinite direct product of finite type systems of each possible Krieger’s type.

Original language	English
Pages (from-to)	1541-1557
Number of pages	17
Journal	Proceedings of the American Mathematical Society
Volume	150
Issue number	4
DOIs	https://doi.org/10.1090/proc/15695
State	Published - 2022

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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title = "KRIEGER{\textquoteright}S TYPE OF NONSINGULAR POISSON SUSPENSIONS AND IDPFT SYSTEMS",

abstract = "Given an infinite countable discrete amenable group Γ, we construct explicitly sharply weak mixing nonsingular Poisson Γ-actions of each Krieger{\textquoteright}s type: IIIλ, for λ ∈ [0, 1], and II∞. The result is new even for Γ = Z. As these Poisson suspension actions are over very special dissipative base, we obtain also new examples of sharply weak mixing nonsingular Bernoulli Γ-actions and infinite direct product of finite type systems of each possible Krieger{\textquoteright}s type.",

author = "Danilenko, \{Alexandre I.\} and Zemer Kosloff",

note = "Publisher Copyright: {\textcopyright} 2022 American Mathematical Society",

year = "2022",

doi = "10.1090/proc/15695",

language = "الإنجليزيّة",

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AU - Danilenko, Alexandre I.

AU - Kosloff, Zemer

PY - 2022

Y1 - 2022

N2 - Given an infinite countable discrete amenable group Γ, we construct explicitly sharply weak mixing nonsingular Poisson Γ-actions of each Krieger’s type: IIIλ, for λ ∈ [0, 1], and II∞. The result is new even for Γ = Z. As these Poisson suspension actions are over very special dissipative base, we obtain also new examples of sharply weak mixing nonsingular Bernoulli Γ-actions and infinite direct product of finite type systems of each possible Krieger’s type.

AB - Given an infinite countable discrete amenable group Γ, we construct explicitly sharply weak mixing nonsingular Poisson Γ-actions of each Krieger’s type: IIIλ, for λ ∈ [0, 1], and II∞. The result is new even for Γ = Z. As these Poisson suspension actions are over very special dissipative base, we obtain also new examples of sharply weak mixing nonsingular Bernoulli Γ-actions and infinite direct product of finite type systems of each possible Krieger’s type.

UR - https://www.scopus.com/pages/publications/85124604936

U2 - 10.1090/proc/15695

DO - 10.1090/proc/15695

M3 - مقالة

SN - 0002-9939

VL - 150

SP - 1541

EP - 1557

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 4

ER -

KRIEGER’S TYPE OF NONSINGULAR POISSON SUSPENSIONS AND IDPFT SYSTEMS

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