An Outline of Ergodic Theory
An Outline of Ergodic Theory
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GBPThis 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.
- 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
'… explains the main ideas and topics of ergodic theory for those readers who want a basic overview of it and who do not want to be overburdened with notions and details. It also gives professional mathematicians familiar with the material the option of a quick review of it.' Mathematical Reviews
Product details
March 2010Hardback
9780521194402
182 pages
235 × 157 × 15 mm
0.38kg
305 exercises
Available
Table of Contents
- Preface
- Introduction
- 1. Measure-theoretic preliminaries
- 2. Measure preserving systems, stationary processes
- 3. Martingales and coupling
- 4. Entropy
- 5. Bernoulli transformations
- 6. Ornstein isomorphism theorem
- 7. Varieties of mixing
- Appendix
- References
- Index.
