Weakly wandering sequences in ergodic theory
By: Stanley Eigen, Arshag Hajian, Yuji Ito, Vidhu Prasad
Contributors: Kakutani, Shizuo, 1911-2004, dedicatee; Hajian, Arshag, author; Itō, Yūji, 1935- author; Prasad, Vidhu, author
Series: Springer monographs in mathematics; Springer monographs in mathematics
Publisher: Springer
Published: 2014
Place of publication: Tokyo; New York
Language: eng
Number of pages: 153
ISBN-13: 9784431551072; 9784431551089
Copyright date: 2014
Subjects: Ergodic theory
Description: The appearance of weakly wandering (ww) sets and sequences for ergodic transformations over half a century ago was an unexpected and surprising event. In time it was shown that ww and related sequences reflected significant and deep properties of ergodic transformations that preserve an infinite measure. This monograph studies in a systematic way the role of ww and related sequences in the classification of ergodic transformations preserving an infinite measure. Connections of these sequences to additive number theory and tilings of the integers are also discussed. The material presented is self-contained and accessible to graduate students. A basic knowledge of measure theory is adequate for the reader. --
Notes: "This monograph is dedicated to Professor Shizuo Kakutani, 1911-2004."

Includes bibliographical references (pages 147-149) and index.
Table of contents: title: 1. Existence of finite invariant measure; title: 2. Transformations with no finite invariant measure; title: 3. Infinite ergodic transformations; title: 4. Three basic examples; title: 5. Properties of various sequences; title: 6. Isomorphism invariants; title: 7. Integer tilings.