On the K property for Maharam extensions of Bernoulli shifts and a question of Krengel

2012/02/08 by Zemer Kosloff, Kosloff, Zemer
Mathematics · #37A20 #37A40 #Advanced Topics in Algebra #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #math.DS #msc:37A20 #msc:37A40

paper · pdf · doi:10.48550/arxiv.1202.1788

Added a section on countable alphabets, to appear in the Israel Journal of Mathematics

openalex publication_date 2012/02/08 · arxiv created 2012/11/14 · arxiv updated 2012/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the Maharam extension of a conservative. non singular K Bernoulli shift without an a.c.i.p. is a K transformation. This together with the fact that the Maharam extension of a conservative transformation is conservative gives a negative answer to Krengel's and Weiss's questions about existence of a type II_∞ or type III_λwith λnot equal to 1 Bernoulli shift. A conservative non singular K Bernoulli shift is either of type II₁ or of type III₁.

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