Fundamentals of measurable dynamics: ergodic theory on Lebesgue spaces
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Clarendon Press
1990
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| Series: | Oxford science publications
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 168 S. |
| ISBN: | 0198535724 |
Staff View
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Record in the Search Index
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|---|---|
| adam_text | Contents
1. Measurable dynamics
1.1 Examples 1
1.2 Exercises 7
2. Lebesgue probability spaces
2.1 Countable algebras and trees of partitions 9
2.2 Generating trees and additive set functions 10
2.3 Lebesgue spaces 12
2.4 A martingale theorem and conditional expectation 18
2.5 More about generating trees and dynamical systems 25
3. Ergodic theorems and ergodic decomposition
3.1 Von Neumann s L2 ergodic theorem 27
3.2 Two proofs of Birkhoff s ergodic theorem 29
3.3 Proof of the backward Vitali lemma 37
3.4 Consequences of the Birkhoff theorem 43
3.5 Disintegrating a measure space over a factor algebra 45
4. Mixing properties
4.1 Poincare recurrence 51
4.2 Ergodicity as a mixing property 51
4.3 Weakly mixing 52
4.4 A little spectral theory 57
4.5 Weakly mixing and eigenfunctions 62
4.6 Mixing 66
4.7 The Kolmogorov Property 69
5. Entropy
5.1 Counting names 71
5.2 The Shannon McMillan Breiman theorem 77
5.3 Entropy zero and past algebras 79
5.4 More about the K property 82
5.5 The entropy of an ergodic transformation 83
5.6 Examples of entropy computations 85
5.7 Entropy and information from the entropy formula 89
5.8 More about zero entropy and tail fields 94
x I Contents
5.9 Even more about the X property 97
5.10 Entropy for non ergodic maps 103
6. Joinings and disjointness
6.1 Joinings 105
6.2 The relatively independent joining 108
6.3 Disjointness 113
6.4 Minimal self joinings 116
6.5 Chacon s map once more 118
6.6 Constructions 125
7. The Krieger and Ornstein theorems
7.1 Symbolic spaces and processes 129
7.2 Painting names on towers and generic names 132
7.3 The ^ Metric and entropy 135
7.4 Pure columns and Ornstein s fundamental lemma 141
7.5 Krieger s finite generator theorem 150
7.6 Ornstein s isomorphism theorem 152
7.7 Weakly Bernoulli processes 156
Bibliography 164
Index 167
|
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| indexdate | 2024-07-09T16:14:31Z |
| institution | BVB |
| isbn | 0198535724 |
| language | English |
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| physical | X, 168 S. |
| publishDate | 1990 |
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| series2 | Oxford science publications |
| spelling | Rudolph, Daniel J. Verfasser aut Fundamentals of measurable dynamics ergodic theory on Lebesgue spaces Daniel J. Rudolph Oxford Clarendon Press 1990 X, 168 S. txt rdacontent n rdamedia nc rdacarrier Oxford science publications Théorie ergodique ram Ergodic theory Measure-preserving transformations Systemtheorie (DE-588)4058812-9 gnd rswk-swf Lebesgue-Maß (DE-588)4240914-7 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Ergodentheorie (DE-588)4015246-7 gnd rswk-swf Lebesgue-Maß (DE-588)4240914-7 s Ergodentheorie (DE-588)4015246-7 s DE-604 Systemtheorie (DE-588)4058812-9 s Dynamisches System (DE-588)4013396-5 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002814139&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rudolph, Daniel J. Fundamentals of measurable dynamics ergodic theory on Lebesgue spaces Théorie ergodique ram Ergodic theory Measure-preserving transformations Systemtheorie (DE-588)4058812-9 gnd Lebesgue-Maß (DE-588)4240914-7 gnd Dynamisches System (DE-588)4013396-5 gnd Ergodentheorie (DE-588)4015246-7 gnd |
| subject_GND | (DE-588)4058812-9 (DE-588)4240914-7 (DE-588)4013396-5 (DE-588)4015246-7 |
| title | Fundamentals of measurable dynamics ergodic theory on Lebesgue spaces |
| title_auth | Fundamentals of measurable dynamics ergodic theory on Lebesgue spaces |
| title_exact_search | Fundamentals of measurable dynamics ergodic theory on Lebesgue spaces |
| title_full | Fundamentals of measurable dynamics ergodic theory on Lebesgue spaces Daniel J. Rudolph |
| title_fullStr | Fundamentals of measurable dynamics ergodic theory on Lebesgue spaces Daniel J. Rudolph |
| title_full_unstemmed | Fundamentals of measurable dynamics ergodic theory on Lebesgue spaces Daniel J. Rudolph |
| title_short | Fundamentals of measurable dynamics |
| title_sort | fundamentals of measurable dynamics ergodic theory on lebesgue spaces |
| title_sub | ergodic theory on Lebesgue spaces |
| topic | Théorie ergodique ram Ergodic theory Measure-preserving transformations Systemtheorie (DE-588)4058812-9 gnd Lebesgue-Maß (DE-588)4240914-7 gnd Dynamisches System (DE-588)4013396-5 gnd Ergodentheorie (DE-588)4015246-7 gnd |
| topic_facet | Théorie ergodique Ergodic theory Measure-preserving transformations Systemtheorie Lebesgue-Maß Dynamisches System Ergodentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002814139&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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