An outline of ergodic theory / Steven Kalikow, Randall McCutcheon.

Format:

Book

Author/Creator:

Kalikow, Steven, 1950- author.

McCutcheon, Randall, 1965- author.

Series:

Cambridge studies in advanced mathematics ; 122.

Cambridge studies in advanced mathematics ; 122

Language:

English

Subjects (All):

Ergodic theory.

Isomorphisms (Mathematics).

Physical Description:

1 online resource (viii, 174 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2010.

Language Note:

English

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.

Contents:

Machine generated contents note: 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.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

ISBN:

1-107-20474-7

1-282-53890-X

9786612538902

0-511-80160-2

0-511-67823-1

0-511-67697-2

0-511-68146-1

0-511-68344-8

0-511-67948-3

OCLC:

648733423