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  3. An Outline of Ergodic Theory
  • Cited by 15
Publisher:
Cambridge University Press
Online publication date:
June 2012
Print publication year:
2010
Online ISBN:
9780511801600
DOI:
https://doi.org/10.1017/CBO9780511801600
Subjects:
Mathematics (general), Mathematics, Communications and Signal Processing, Engineering, Discrete Mathematics Information Theory and Coding
Series:
Cambridge Studies in Advanced Mathematics (122)
Information

Book description

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.

Reviews

'… 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.'

Source: Mathematical Reviews

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