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An Introduction to Infinite Ergodic Theory
Jon Aaronson, Tel Aviv University, Israel

Mathematical Surveys and Monographs
1997; 284 pp; hardcover
Volume: 50
ISBN-10: 0-8218-0494-4
ISBN-13: 978-0-8218-0494-0
List Price: US$101
Member Price: US$80.80
Order Code: SURV/50
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Infinite ergodic theory is the study of measure preserving transformations of infinite measure spaces. The book focuses on properties specific to infinite measure preserving transformations.

The work begins with an introduction to basic nonsingular ergodic theory, including recurrence behavior, existence of invariant measures, ergodic theorems, and spectral theory. A wide range of possible "ergodic behavior" is catalogued in the third chapter mainly according to the yardsticks of intrinsic normalizing constants, laws of large numbers, and return sequences. The rest of the book consists of illustrations of these phenomena, including Markov maps, inner functions, and cocycles and skew products. One chapter presents a start on the classification theory.


Graduate students and research mathematicians interested in ergodic theory, dynamical systems and/or probability.


"This book is a research monograph and contains an impressive amount of material. The presentation is careful, well organized, and reliable. This monograph is definitely a valuable complement to the ergodic theory literature. It will be useful to graduate students and researchers in ergodic theory and related fields."

-- Bulletin of the London Mathematical Society

"Accessible to readers with a firm background in measure-theoretic probability ... carefully organized and well written ... invaluable both as an introduction and as a reference work on its subject, and this definitely is not just because it is the only one at the moment."

-- Zentralblatt MATH

"This book is devoted mainly to the ergodic theory of transformations preserving an infinite measure, and as such it is a welcome addition to the literature. [O]verall this book fills important gaps in the literature and is recommended to researchers and advanced students."

-- Mathematical Reviews

Table of Contents

  • Non-singular transformations
  • General ergodic and spectral theorems
  • Transformations with infinite invariant measures
  • Markov maps
  • Recurrent events and similarity of Markov shifts
  • Inner functions
  • Hyperbolic geodesic flows
  • Cocycles and skew products
  • Bibliography
  • Index
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