Abstract
We show here that a finite extension of a Bernoulli shift either has a finite rotation factor or is Bernoulli. The proof lifts to this more general case the “nesting” technique we used previously to prove this for two point extensions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
D. S. Ornstein,Factors of a Bernoulli shift, Israel J. Math.21 (1975), 145–153.
W. Parry,Ergodic properties of affine transformations and flows on nilmanifolds, Amer. J. Math.91 (1969), 757–771.
D. J. Rudolph,If a two-point extension of a Bernoulli shift has an ergodic square, then it is Bernoulli, Israel J. Math., in press.
J. P. Thouvenout,Quelques propriétés des systèmes dynamiques se décomposent en un produit de deux systémes dont l’un est un schéma de Bernoulli. Israel J. Math.21 (1975), 177–207.
B. Weiss,Equivalence of Measure Preserving Transformations, Lecture Notes, The Institute for Advanced Studies, The Hebrew University of Jerusalem, 1976.
Author information
Authors and Affiliations
Additional information
This work was supported by the Miller Institute for Basic Research.
Rights and permissions
About this article
Cite this article
Rudolph, D.J. If a finite extension of a Bernoulli shift has no finite rotation factors, it is Bernoulli. Israel J. Math. 30, 193–206 (1978). https://doi.org/10.1007/BF02761070
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02761070