An Outline of Ergodic Theory

Erscheinungsjahr 2010
ISBN: 978-0-521-19440-2
Verlag: Cambridge University Press

Buch, Englisch, Band 122, 182 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 426 g

Reihe: Cambridge Studies in Advanced Mathematics

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.

Autoren/Hrsg.

Kalikow, Steven

McCutcheon, Randall

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse

Inhaltsverzeichnis

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.

Über Autor(innen)

Kalikow, Steven
Steven Kalikow is a Visiting Professor in the Department of Mathematical Sciences at the University of Memphis.

McCutcheon, Randall
Randall McCutcheon is Assistant Professor in the Department of Mathematical Sciences at the University of Memphis.