Infinite ergodic theory is the study of measure preserving transformations of infinite measure spaces. This 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.
| ISBN: | 9780821804940 |
| Publication date: | 30th May 1997 |
| Author: | Jon Aaronson |
| Publisher: | American Mathematical Society |
| Format: | Hardback |
| Pagination: | 284 pages |
| Series: | Mathematical Surveys and Monographs |
| Genres: |
Calculus and mathematical analysis Applied mathematics |