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Published in:
2019 | OriginalPaper | Chapter
1. Introduction
Authors : Gabriel Ponce, Régis Varão
Published in: An Introduction to the Kolmogorov–Bernoulli Equivalence
Publisher: Springer International Publishing
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Abstract
In this chapter we briefly motivate the main theme of this book: the Kolmogorov–Bernoulli equivalence problem. We introduce the idea behind the ergodic hierarchy of measure preserving transformations and quickly discuss the problem of detecting conditions under which the Kolmogorov property is promoted to the Bernoulli property. In particular the method introduced by Ornstein and Weiss is of particular interest for our context (smooth dynamics).