An Outline of Ergodic Theory
(Sprache: Englisch)
This informal introduction focuses on the branch of ergodic theory known as isomorphism theory. Exercises, open problems, and helpful hints actively engage the reader and encourage them to participate in developing proofs independently. Ideal for graduate...
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This informal introduction focuses on the branch of ergodic theory known as isomorphism theory. Exercises, open problems, and helpful hints actively engage the reader and encourage them to participate in developing proofs independently. Ideal for graduate courses, this book is also a valuable reference for the professional mathematician.
Klappentext zu „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 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.
Inhaltsverzeichnis zu „An Outline of Ergodic Theory “
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.
Autoren-Porträt von Steven Kalikow, Randall McCutcheon
Kalikow, StevenSteven Kalikow is a Visiting Professor in the Department of Mathematical Sciences at the University of Memphis.
Bibliographische Angaben
- Autoren: Steven Kalikow , Randall McCutcheon
- 2010, 182 Seiten, Maße: 23,5 cm, Gebunden, Englisch
- Verlag: Cambridge University Press
- ISBN-10: 0521194407
- ISBN-13: 9780521194402
Sprache:
Englisch
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