An Outline of Ergodic Theory

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Overview

This informal introduction provides a fresh perspective on isomorphism theory, which is the branch of ergodic theory that explores the conditions under which two measure preserving systems are essentially equivalent. It contains a primer in basic measure theory, proofs of fundamental ergodic theorems, and material on entropy, martingales, Bernoulli processes, and various varieties of mixing. Original proofs of classic theorems - including the Shannon-McMillan-Breiman theorem, the Krieger finite generator theorem, and the Ornstein isomorphism theorem - are presented by degrees, together with helpful hints that encourage the reader to develop the proofs on their own. Hundreds of exercises and open problems are also included, making this an ideal text for graduate courses. Professionals needing a quick review, or seeking a different perspective on the subject, will also value this book.

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Editorial Reviews

From the Publisher
"The book under review is very useful. On the one hand, the way of presenting the material is intuitive; on the other hand, it enables the reader to understand ergodic theory more deeply."
Jan Kwiatkowski, Mathematical Reviews
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Product Details

Meet the Author

Steven Kalikow is a Visiting Professor in the Department of Mathematical Sciences at the University of Memphis.

Randall McCutcheon is Assistant Professor in the Department of Mathematical Sciences at the University of Memphis.

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Table of Contents

Introduction 1

1 Measure-theoretic preliminaries 5

2 Measure-preserving systems, stationary processes 26

3 Martingales and coupling 55

4 Entropy 72

5 Bernoulli transformations 96

6 Ornstein isomorphism theorem 124

7 Varieties of mixing 146

Appendix 167

References 170

Index 173

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