Invitation to ergodic theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
2008
|
| Series: | Student mathematical library
volume 42 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | ix, 262 Seiten Illustrationen, Diagramme 22 cm |
| ISBN: | 9780821844205 |
Staff View
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| 100 | 1 | |a Silva, Ceśar Ernesto |d 1955- |e Verfasser |0 (DE-588)141995688 |4 aut | |
| 245 | 1 | 0 | |a Invitation to ergodic theory |c C. E. Silva |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c 2008 | |
| 264 | 4 | |c © 2008 | |
| 300 | |a ix, 262 Seiten |b Illustrationen, Diagramme |c 22 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Student mathematical library |v volume 42 | |
| 650 | 4 | |a Lebesgue, Intégrale de | |
| 650 | 4 | |a Théorie ergodique | |
| 650 | 4 | |a Ergodic theory | |
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Record in the Search Index
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| adam_text | INVITATION TO ERGODIC THEORY C. E. SILVA SUB GOTTINGEN 7 221 904 859
2008 A 252 IAMS AMERICAN MATHEMATICAL SOCIETY PROVIDENCE, RHODE ISLAND
CONTENTS PREFACE VII CHAPTER 1. INTRODUCTION 1 CHAPTER 2. LEBESGUE
MEASURE 5 §2.1. LEBESGUE OUTER MEASURE 5 §2.2. THE CANTOR SET AND NULL
SETS 10 §2.3. LEBESGUE MEASURABLE SETS 17 §2.4. COUNTABLE ADDITIVITY 23
§2.5. SIGMA-ALGEBRAS AND MEASURE SPACES 26 §2.6. THE BOREL SIGMA-ALGEBRA
34 §2.7. APPROXIMATION WITH SEMI-RINGS 38 §2.8. MEASURES FROM OUTER
MEASURES 47 CHAPTER 3. RECURRENCE AND ERGODICITY 59 §3.1. AN EXAMPLE:
THE BAKER S TRANSFORMATION 60 §3.2. ROTATION TRANSFORMATIONS 67 §3.3.
THE DOUBLING MAP: A BERNOULLI NONINVERTIBLE TRANSFORMATION 75 §3.4.
MEASURE-PRESERVING TRANSFORMATIONS 83 §3.5. RECURRENCE 86 III IV
CONTENTS §3.6. ALMOST EVERYWHERE AND INVARIANT SETS 91 §3.7. ERGODIC
TRANSFORMATIONS 95 §3.8. THE DYADIC ODOMETER 102 §3.9. INFINITE
MEASURE-PRESERVING TRANSFORMATIONS 109 §3.10. FACTORS AND ISOMORPHISM
115 §3.11. THE INDUCED TRANSFORMATION 120 §3.12. SYMBOLIC SPACES 123
§3.13. SYMBOLIC SYSTEMS 127 CHAPTER 4. THE LEBESGUE INTEGRAL 131 §4.1.
THE RIEMANN INTEGRAL 131 §4.2. MEASURABLE FUNCTIONS 134 §4.3. THE
LEBESGUE INTEGRAL OF SIMPLE FUNCTIONS 141 §4.4. THE LEBESGUE INTEGRAL OF
NONNEGATIVE FUNCTIONS 145 §4.5. APPLICATION: THE GAUSS TRANSFORMATION
150 §4.6. LEBESGUE INTEGRABLE FUNCTIONS 155 §4.7. THE LEBESGUE SPACES:
L L 2 AND L 159 §4.8. EIGENVALUES 166 §4.9. PRODUCT MEASURE 170
CHAPTER 5. THE ERGODIC THEOREM 175 §5.1. THE BIRKHOFF ERGODIC THEOREM
176 §5.2. NORMAL NUMBERS 188 §5.3. WEYL EQUIDISTRIBUTION 191 §5.4. THE
MEAN ERGODIC THEOREM 192 CHAPTER 6. MIXING NOTIONS 201 §6.1.
INTRODUCTION 201 §6.2. WEAK MIXING 205 §6.3. APPROXIMATION 209 §6.4.
CHARACTERIZATIONS OF WEAK MIXING 214 §6.5. CHACON S TRANSFORMATION 218
§6.6. MIXING 226 CONTENTS §6.7. RIGIDITY AND MILD MIXING 227 §6.8. WHEN
APPROXIMATION FAILS 231 APPENDIX A. SET NOTATION AND THE COMPLETENESS OF
M 235 APPENDIX B. TOPOLOGY OF M AND METRIC SPACES 241 BIBLIOGRAPHICAL
NOTES 251 BIBLIOGRAPHY 255 INDEX 259
|
| adam_txt |
INVITATION TO ERGODIC THEORY C. E. SILVA SUB GOTTINGEN 7 221 904 859
2008 A 252 IAMS AMERICAN MATHEMATICAL SOCIETY PROVIDENCE, RHODE ISLAND
CONTENTS PREFACE VII CHAPTER 1. INTRODUCTION 1 CHAPTER 2. LEBESGUE
MEASURE 5 §2.1. LEBESGUE OUTER MEASURE 5 §2.2. THE CANTOR SET AND NULL
SETS 10 §2.3. LEBESGUE MEASURABLE SETS 17 §2.4. COUNTABLE ADDITIVITY 23
§2.5. SIGMA-ALGEBRAS AND MEASURE SPACES 26 §2.6. THE BOREL SIGMA-ALGEBRA
34 §2.7. APPROXIMATION WITH SEMI-RINGS 38 §2.8. MEASURES FROM OUTER
MEASURES 47 CHAPTER 3. RECURRENCE AND ERGODICITY 59 §3.1. AN EXAMPLE:
THE BAKER'S TRANSFORMATION 60 §3.2. ROTATION TRANSFORMATIONS 67 §3.3.
THE DOUBLING MAP: A BERNOULLI NONINVERTIBLE TRANSFORMATION 75 §3.4.
MEASURE-PRESERVING TRANSFORMATIONS 83 §3.5. RECURRENCE 86 III IV
CONTENTS §3.6. ALMOST EVERYWHERE AND INVARIANT SETS 91 §3.7. ERGODIC
TRANSFORMATIONS 95 §3.8. THE DYADIC ODOMETER 102 §3.9. INFINITE
MEASURE-PRESERVING TRANSFORMATIONS 109 §3.10. FACTORS AND ISOMORPHISM
115 §3.11. THE INDUCED TRANSFORMATION 120 §3.12. SYMBOLIC SPACES 123
§3.13. SYMBOLIC SYSTEMS 127 CHAPTER 4. THE LEBESGUE INTEGRAL 131 §4.1.
THE RIEMANN INTEGRAL 131 §4.2. MEASURABLE FUNCTIONS 134 §4.3. THE
LEBESGUE INTEGRAL OF SIMPLE FUNCTIONS 141 §4.4. THE LEBESGUE INTEGRAL OF
NONNEGATIVE FUNCTIONS 145 §4.5. APPLICATION: THE GAUSS TRANSFORMATION
150 §4.6. LEBESGUE INTEGRABLE FUNCTIONS 155 §4.7. THE LEBESGUE SPACES:
L\L 2 AND L 159 §4.8. EIGENVALUES 166 §4.9. PRODUCT MEASURE 170
CHAPTER 5. THE ERGODIC THEOREM 175 §5.1. THE BIRKHOFF ERGODIC THEOREM
176 §5.2. NORMAL NUMBERS 188 §5.3. WEYL EQUIDISTRIBUTION 191 §5.4. THE
MEAN ERGODIC THEOREM 192 CHAPTER 6. MIXING NOTIONS 201 §6.1.
INTRODUCTION 201 §6.2. WEAK MIXING 205 §6.3. APPROXIMATION 209 §6.4.
CHARACTERIZATIONS OF WEAK MIXING 214 §6.5. CHACON'S TRANSFORMATION 218
§6.6. MIXING 226 CONTENTS §6.7. RIGIDITY AND MILD MIXING 227 §6.8. WHEN
APPROXIMATION FAILS 231 APPENDIX A. SET NOTATION AND THE COMPLETENESS OF
M 235 APPENDIX B. TOPOLOGY OF M AND METRIC SPACES 241 BIBLIOGRAPHICAL
NOTES 251 BIBLIOGRAPHY 255 INDEX 259 |
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| isbn | 9780821844205 |
| language | English |
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| spelling | Silva, Ceśar Ernesto 1955- Verfasser (DE-588)141995688 aut Invitation to ergodic theory C. E. Silva Providence, Rhode Island American Mathematical Society 2008 © 2008 ix, 262 Seiten Illustrationen, Diagramme 22 cm txt rdacontent n rdamedia nc rdacarrier Student mathematical library volume 42 Lebesgue, Intégrale de Théorie ergodique Ergodic theory Ergodentheorie (DE-588)4015246-7 gnd rswk-swf Ergodentheorie (DE-588)4015246-7 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-2151-9 Student mathematical library volume 42 (DE-604)BV013184751 42 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016486933&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Silva, Ceśar Ernesto 1955- Invitation to ergodic theory Student mathematical library Lebesgue, Intégrale de Théorie ergodique Ergodic theory Ergodentheorie (DE-588)4015246-7 gnd |
| subject_GND | (DE-588)4015246-7 |
| title | Invitation to ergodic theory |
| title_auth | Invitation to ergodic theory |
| title_exact_search | Invitation to ergodic theory |
| title_exact_search_txtP | Invitation to ergodic theory |
| title_full | Invitation to ergodic theory C. E. Silva |
| title_fullStr | Invitation to ergodic theory C. E. Silva |
| title_full_unstemmed | Invitation to ergodic theory C. E. Silva |
| title_short | Invitation to ergodic theory |
| title_sort | invitation to ergodic theory |
| topic | Lebesgue, Intégrale de Théorie ergodique Ergodic theory Ergodentheorie (DE-588)4015246-7 gnd |
| topic_facet | Lebesgue, Intégrale de Théorie ergodique Ergodic theory Ergodentheorie |
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