エルゴード理論概説 An Outline of Ergodic Theory (Cambridge Studies in Advanced Mathematics)

Kalikow, Steven/ McCutcheon, Randall

Cambridge University Press（2010/03発売）

• 製本 Hardcover:ハードカバー版／ページ数 182 p.
• 言語 ENG
• 商品コード 9780521194402
• DDC分類 515.48

基本説明

Ideal for graduate courses, this book is also a valuable reference for the professional mathematician.

Full 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.

Contents

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.