An outline of ergodic theory

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 theorem...

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Main Authors: Kalikow, Steven, McCutcheon, Randall (Author)
Format: eBook
Language:English
Published: Cambridge Cambridge University Press 2010
Series:Cambridge studies in advanced mathematics
Subjects:
Online Access:
Collection: Cambridge Books Online - Collection details see MPG.ReNa
Summary: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
Physical Description:viii, 174 pages digital
ISBN:9780511801600