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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.Read more
- Encourages readers to actively participate in the development of proofs
- Contains original proofs of classic theorems in ergodic theory
- Easily navigable for experts requiring only a quick review
Reviews & endorsements
"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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- Date Published: April 2010
- format: Hardback
- isbn: 9780521194402
- length: 182 pages
- dimensions: 235 x 157 x 15 mm
- weight: 0.38kg
- contains: 305 exercises
- availability: In stock
Table of Contents
1. Measure-theoretic preliminaries
2. Measure preserving systems, stationary processes
3. Martingales and coupling
5. Bernoulli transformations
6. Ornstein isomorphism theorem
7. Varieties of mixing
Instructors have used or reviewed this title for the following courses
- Advanced Stochastic Process
- Ergodic Theory
- Statistical Machine Learning
- information theory and coding
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