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

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

2012-02-08

arxiv.org/abs/1202.1788v1

Mathematics

Dynamical Systems

This research was was supported by THE ISF grant No. 1114/08

Scientific paper

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}_\infty or type III}_\lambda with \lambda not equal to 1 Bernoulli shift. A conservative non singular K Bernoulli shift is either of type II_1 or of type III_1.

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