A radical approach to Lebesgue's theory of integration:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2008
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | MAA textbooks
|
| Schlagwörter: | |
| Links: | http://www.loc.gov/catdir/enhancements/fy0803/2007035326-t.html http://www.loc.gov/catdir/enhancements/fy0803/2007035326-d.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016532837&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Includes bibliographical references (p. 317-322) and index |
| Umfang: | xiv, 329 p. ill. 26 cm |
| ISBN: | 9780521884747 0521884748 9780521711838 0521711835 |
Internformat
MARC
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| 245 | 1 | 0 | |a A radical approach to Lebesgue's theory of integration |c David M. Bressoud |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 2008 | |
| 300 | |a xiv, 329 p. |b ill. |c 26 cm | ||
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 280f 2016 B 1813 |
|---|---|
| DE-BY-TUM_katkey | 2224939 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040008247432 |
| _version_ | 1821935445167046656 |
| adam_text | Contents
ice page xi
Introduction 1
1.1 The Five Big Questions 2
1.2 Presumptions 15
The Riemann Integral 23
2.1 Existence 24
2.2 Nondifferentiable Integrals 33
2.3 The Class of 1870 40
Explorations of R 51
3.1 Geometry of K 51
3.2 Accommodating Algebra 59
3.3 Set Theory 71
Nowhere Dense Sets and the Problem with the Fundamental
Theorem of Calculus 81
4.1 The Smith-Volterra-Cantor Sets 82
4.2 Volterra s Function 89
4.3 Term-by-Term Integration 98
4.4 The Baire Category Theorem 109
The Development of Measure Theory 120
5.1 Peano, Jordan, and Borel 122
5.2 Lebesgue Measure 131
5.3 Carathéodory s Condition 140
5.4 Nonmeasurable Sets 150
The Lebesgue Integral 159
6.1 Measurable Functions 159
6.2 Integration 169
6.3 Lebesgue s Dominated Convergence Theorem 183
6.4 Egorov s Theorem 191
IX
x Contents
7 The Fundamental Theorem of Calculus 203
7.1 The Dini Derivatives 204
7.2 Monotonicity Implies Differentiability Almost Everywhere 212
7.3 Absolute Continuity 223
7.4 Lebesgue s FTC 231
8 Fourier Series 241
8.1 Pointwise Convergence 242
8.2 Metric Spaces 251
8.3 Banach Spaces 263
8.4 Hilbert Spaces 271
9 Epilogue 282
Appendixes 287
A Other Directions 287
A. 1 The Cardinality of the Collection of Borel Sets 287
A.2 The Generalized Riemann Integral 291
B Hints to Selected Exercises 299
Bibliography 317
Index 323
|
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| id | DE-604.BV023349199 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T13:14:12Z |
| institution | BVB |
| isbn | 9780521884747 0521884748 9780521711838 0521711835 |
| language | English |
| lccn | 2007035326 |
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| physical | xiv, 329 p. ill. 26 cm |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Cambridge University Press |
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| series2 | MAA textbooks |
| spellingShingle | Bressoud, David M. 1950- A radical approach to Lebesgue's theory of integration Integrals, Generalized Lebesgue-Integral (DE-588)4034949-4 gnd |
| subject_GND | (DE-588)4034949-4 |
| title | A radical approach to Lebesgue's theory of integration |
| title_auth | A radical approach to Lebesgue's theory of integration |
| title_exact_search | A radical approach to Lebesgue's theory of integration |
| title_full | A radical approach to Lebesgue's theory of integration David M. Bressoud |
| title_fullStr | A radical approach to Lebesgue's theory of integration David M. Bressoud |
| title_full_unstemmed | A radical approach to Lebesgue's theory of integration David M. Bressoud |
| title_short | A radical approach to Lebesgue's theory of integration |
| title_sort | a radical approach to lebesgue s theory of integration |
| topic | Integrals, Generalized Lebesgue-Integral (DE-588)4034949-4 gnd |
| topic_facet | Integrals, Generalized Lebesgue-Integral |
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Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 MAT 280f 2016 B 1813 Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |