Ergodic theorems /
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| Author / Creator: | Krengel, Ulrich, 1937- |
|---|---|
| Imprint: | Berlin ; New York : Walter de Gruyter, 1985. |
| Description: | 1 online resource (vii, 357 pages) |
| Language: | English |
| Series: | De Gruyter studies in mathematics ; 6 De Gruyter studies in mathematics ; 6. |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11382479 |
Table of Contents:
- 2.4 The splitting theorem of Jacobs-Deleeuw-GlicksbergChapter 3: Positive contractions in L1; 3.1 The Hopf decomposition; 3.2 The Chacon-Ornstein theorem; 3.3 Brunel's lemma and the identification of the limit; 3.4 Existence of finite invariant measures; 3.5 The subadditive ergodic theorem for positive contractions in L1; 3.6 An example with divergence of Cesà€ro averages; 3.7 More on the filling scheme; Chapter 4: Extensions of the L1-theory; 4.1 Non positive contractions in L1; 4.2 Vector valued ergodic theorems; 4.3 Power bounded operators and harmonic functions.
- 7.2 Local ergodic theorems for multiparameter and non positive semigroups, and for vector valued functionsChapter 8: Subsequences and generalized means; 8.1 Strong convergence and mixing; 8.2 Pointwise convergence; Chapter 9: Special topics; 9.1 Ergodic theorems in von Neumann algebras; 9.2 Entropy and information; 9.3 Nonlinear nonexpansive mappings; 9.4 Miscellanea; Supplement: Harris Processes, Special Functions, Zero-Two-Law (by Antoine Brunei); Bibliography; Notation; Index.
- Chapter 1: Measure preserving and null preserving point mappings; 1.1 Von Neumann's mean ergodic theorem, ergodicity; 1.2 Birkhoff's ergodic theorem; 1.3 Recurrence; 1.4 Shift transformations and stationary processes; 1.5 Kingman's subadditive ergodic theorem and the multiplicative ergodic theorem of Oseledec; 1.6 Relatives of the maximal ergodic theorem; 1.7 Some general tools and principles; Chapter 2: Mean ergodic theory; 2.1 The mean ergodic theorem; 2.2 Uniform convergence; 2.3 Weak mixing, continuous spectrum and multiple recurrence.