A (terse) introduction to Lebesgue integration:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
2009
|
| Schriftenreihe: | Student mathematical library
48 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XVI, 202 S. |
| ISBN: | 9780821848623 |
Internformat
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| 100 | 1 | |a Franks, John M. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a A (terse) introduction to Lebesgue integration |c John Franks |
| 246 | 1 | 3 | |a Introduction to Lebesgue integration |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2009 | |
| 300 | |a XVI, 202 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Student mathematical library |v 48 | |
| 500 | |a Includes bibliographical references and index | ||
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Datensatz im Suchindex
| _version_ | 1804140309403140096 |
|---|---|
| adam_text | Titel: A (terse) introduction to Lebesgue integration
Autor: Franks, John M.
Jahr: 2009
Contents
Preface xi
Chapter 1. The Regulated and Riemann Integrals 1
§1.1. Introduction 1
§1.2. Basic Properties of an Integral 2
§1.3. Step Functions 4
§1.4. Uniform and Pointwise Convergence 7
§1.5. Regulated Integral 8
§1.6. The Fundamental Theorem of Calculus 13
§1.7. The Riemann Integral 16
Chapter 2. Lebesgue Measure 25
§2.1. Introduction 25
§2.2. Null Sets 27
§2.3. Sigma Algebras 29
§2.4. Lebesgue Measure 31
§2.5. The Lebesgue Density Theorem 35
§2.6. Lebesgue Measurable Sets - Summary 37
Chapter 3. The Lebesgue Integral 41
§3.1. Measurable Functions 41
vii
Contents
viii
§3.2. The Lebesgue Integral of Bounded Functions
§3.3. The Bounded Convergence Theorem
63
Chapter 4. The Integral of Unbounded Functions
63
§4.1. Non-negative Functions
§4.2. Convergence Theorems
§4.3. Other Measures
77
§4.4. General Measurable Functions
Chapter 5. The Hilbert Space I?
83
§5.1. Square Integrable Functions
89
§5.2. Convergence in L2
§5.3. Hilbert Space 95
§5.4. Fourier Series
§5.5. Complex Hilbert Space 104
Chapter 6. Classical Fourier Series
§6.1. Real Fourier Series lU
§6.2. Integrable Complex-Valued Functions 1
§6.3. The Complex Hilbert Space L^-tt, tt] 122
§6.4. The Hilbert Space L J 125
Chapter 7. Two Ergodic Transformations l2^
§7.1. Measure Preserving Transformations 1 ^
§7.2. Ergodicity 134
§7.3. The Birkhoff Ergodic Theorem 137
Appendix A. Background and Foundations 141
§A.l. The Completeness of M 141
§A.2. Functions and Sequences 143
§A.3. Limits 145
§A.4. Complex Limits 148
§A.5. Set Theory and Countability 151
§A.6. Open and Closed Sets 156
Contents ix
§A.7. Compact Subsets of R 158
§A.8. Continuous and DifFerentiable Functions 160
§A.9. Real Vector Spaces 162
§A.1O. Complex Vector Spaces 166
§A.ll. Complete Normed Vector Spaces 170
Appendix B. Lebesgue Measure 173
§B.l. Introduction 173
§B.2. Outer Measure 174
§B.3. The cr-algebra of Lebesgue Measurable Sets 180
§B.4. The Existence of Lebesgue Measure 189
Appendix C. A Non-measurable Set 193
Bibliography 197
Index 199
|
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| indexdate | 2024-07-09T21:57:56Z |
| institution | BVB |
| isbn | 9780821848623 |
| language | English |
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| series | Student mathematical library |
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| spelling | Franks, John M. Verfasser aut A (terse) introduction to Lebesgue integration John Franks Introduction to Lebesgue integration Providence, RI American Math. Soc. 2009 XVI, 202 S. txt rdacontent n rdamedia nc rdacarrier Student mathematical library 48 Includes bibliographical references and index Lebesgue-Integral (DE-588)4034949-4 gnd rswk-swf Lebesgue-Integral (DE-588)4034949-4 s DE-604 Student mathematical library 48 (DE-604)BV013184751 48 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018338768&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Franks, John M. A (terse) introduction to Lebesgue integration Student mathematical library Lebesgue-Integral (DE-588)4034949-4 gnd |
| subject_GND | (DE-588)4034949-4 |
| title | A (terse) introduction to Lebesgue integration |
| title_alt | Introduction to Lebesgue integration |
| title_auth | A (terse) introduction to Lebesgue integration |
| title_exact_search | A (terse) introduction to Lebesgue integration |
| title_full | A (terse) introduction to Lebesgue integration John Franks |
| title_fullStr | A (terse) introduction to Lebesgue integration John Franks |
| title_full_unstemmed | A (terse) introduction to Lebesgue integration John Franks |
| title_short | A (terse) introduction to Lebesgue integration |
| title_sort | a terse introduction to lebesgue integration |
| topic | Lebesgue-Integral (DE-588)4034949-4 gnd |
| topic_facet | Lebesgue-Integral |
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