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Science China Mathematics

, Volume 62, Issue 1, pp 69–72 | Cite as

Relative weak mixing is generic

  • Eli GlasnerEmail author
  • Benjamin Weiss
Articles
  • 17 Downloads

Abstract

A classical result of Halmos asserts that among measure preserving transformations the weak mixing property is generic. We extend Halmos’ result to the collection of ergodic extensions of a fixed, but arbitrary, aperiodic transformation T0. We then use a result of Ornstein and Weiss to extend this relative theorem to the general (countable) amenable group.

Keywords

relative weak mixing Rokhlin’s lemma amenable groups 

MSC(2010)

37A25 37A05 37A15 37A20 

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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsTel Aviv UniversityTel AvivIsrael
  2. 2.Institute of MathematicsThe Hebrew University of JerusalemJerusalemIsrael

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