Lebesgue integration:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
1995
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 264 S. graph. Darst. |
| ISBN: | 3540943579 0387943579 |
Internformat
MARC
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| 245 | 1 | 0 | |a Lebesgue integration |c Soo Bong Chae |
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| 300 | |a XIII, 264 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804124338930057216 |
|---|---|
| adam_text | Contents
Preface to the Second Edition v
Preface to the First Edition vii
CHAPTER ZERO
Preliminaries 1
1. Sets 1
2. Relations 4
3. Countable Sets 6
4. Real Numbers 8
5. Topological Concepts in R 10
6. Continuous Functions 15
7. Metric Spaces 18
CHAPTER I
The Riemann Integral 24
1. The Cauchy Integral 24
2. Fourier Series and Dirichlet s Conditions 27
3. The Riemann Integral 31
4. Sets of Measure Zero 35
5. Existence of the Riemann Integral 40
6. Deficiencies of the Riemann Integral 44
CHAPTER II
The Lebesgue Integral: Riesz Method 50
1. Step Functions and Their Integrals 51
2. Two Fundamental Lemmas 55
3. The Class L+ 58
4. The Lebesgue Integral 63
xii Contents
5. The Beppo Levi Theorem—Monotone Convergence Theorem 67
6. The Lebesgue Theorem—Dominated Convergence Theorem 73
7. The Space L1 79
Appendix 84
Henri Lebesgue 84
Frigyes Riesz 85
CHAPTER III
Lebesgue Measure 87
1. Measurable Functions 87
2. Lebesgue Measure 90
3. tr Algebras and Borel Sets 94
4. Nonmeasurable Sets 97
5. Structure of Measurable Sets 101
6. More About Measurable Functions 104
7. Egoroff s Theorem 106
8. Steinhaus Theorem 112
9. The Cauchy Functional Equation 115
10. Lebesgue Outer and Inner Measures 118
CHAPTER IV
Generalizations 125
1. The Integral on Measurable Sets 125
2. The Integral on Infinite Intervals 132
3. Lebesgue Measure on R 135
4. Finite Additive Measure: The Banach Measure Problem 139
5. The Double Lebesgue Integral and the Fubini Theorem 143
6. The Complex Integral 152
CHAPTER V
Differentiation and the Fundamental Theorem of Calculus 155
1. Nowhere Differentiable Functions 156
2. The Dini Derivatives 160
3. The Rising Sun Lemma and Differentiability of Monotone Functions 162
4. Functions of Bounded Variation 171
5. Absolute Continuity 178
6. The Fundamental Theorem of Calculus 184
CHAPTER VI
The L Spaces and the Riesz Fischer Theorem 191
1. The Lp Spaces (1 p oo) 191
2. Approximations by Continuous Functions 199
3. The Space LT 205
4. The I Spaces (1 p oo) 209
5. Hilbert Spaces 211
6. The Riesz Fischer Theorem 216
7. Orthonormalization 224
Contents xiii
8. Completeness of the Trigonometric System 226
9. Isoperimetric Problem 229
10. Remarks on Fourier Series 232
APPENDIX
The Development of the Notion of the Integral
by Henri Lebesgue 234
Bibliography 249
Notation 254
Index 257
|
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| discipline | Mathematik |
| edition | 2. ed. |
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| id | DE-604.BV009965658 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:44:05Z |
| institution | BVB |
| isbn | 3540943579 0387943579 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006605164 |
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| physical | XIII, 264 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Springer |
| record_format | marc |
| series2 | Universitext |
| spelling | Chae, Soo Bong Verfasser aut Lebesgue integration Soo Bong Chae 2. ed. New York [u.a.] Springer 1995 XIII, 264 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext Intégrales généralisées ram Lebesgue, Intégrale de Lebesgue, Intégrale de ram Lebesgue-integralen gtt Lebesgue integral Integrationstheorie (DE-588)4138369-2 gnd rswk-swf Lebesgue-Integral (DE-588)4034949-4 gnd rswk-swf Lebesgue-Integral (DE-588)4034949-4 s DE-604 Integrationstheorie (DE-588)4138369-2 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006605164&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Chae, Soo Bong Lebesgue integration Intégrales généralisées ram Lebesgue, Intégrale de Lebesgue, Intégrale de ram Lebesgue-integralen gtt Lebesgue integral Integrationstheorie (DE-588)4138369-2 gnd Lebesgue-Integral (DE-588)4034949-4 gnd |
| subject_GND | (DE-588)4138369-2 (DE-588)4034949-4 |
| title | Lebesgue integration |
| title_auth | Lebesgue integration |
| title_exact_search | Lebesgue integration |
| title_full | Lebesgue integration Soo Bong Chae |
| title_fullStr | Lebesgue integration Soo Bong Chae |
| title_full_unstemmed | Lebesgue integration Soo Bong Chae |
| title_short | Lebesgue integration |
| title_sort | lebesgue integration |
| topic | Intégrales généralisées ram Lebesgue, Intégrale de Lebesgue, Intégrale de ram Lebesgue-integralen gtt Lebesgue integral Integrationstheorie (DE-588)4138369-2 gnd Lebesgue-Integral (DE-588)4034949-4 gnd |
| topic_facet | Intégrales généralisées Lebesgue, Intégrale de Lebesgue-integralen Lebesgue integral Integrationstheorie Lebesgue-Integral |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006605164&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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