Lebesgue's theory of integration: Its origins and development
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
The Bronx, NY
Chelsea
1975
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 227 S. |
| ISBN: | 0828402825 |
Internformat
MARC
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| 245 | 1 | 0 | |a Lebesgue's theory of integration |b Its origins and development |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a The Bronx, NY |b Chelsea |c 1975 | |
| 300 | |a XV, 227 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 4 | |a Integrals, Generalized | |
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| 650 | 0 | 7 | |a Integration |g Mathematik |0 (DE-588)4072852-3 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804116412424257536 |
|---|---|
| adam_text | Contents
Introduction ix
Chapter 1 Riemann s Theory of Integration 3
1.1 The Eighteenth Century Conception of a
Function and Trigonometric Series Repre¬
sentations, 3
1.2 Cauchy s Conception of the Integral, 9
1.3 Dirichlet s Contribution, 12
1.4 Riemann, 16
Chapter 2 The Development of Riemann s Ideas: 1870 80 21
2.1 Trigonometric Series and Term by Term In¬
tegration, 21
2.2 The Reformulation of Riemann s Integra
bility Criteria, 28
2.3 Discussions of the Differentiability Prop¬
erties of Continuous Functions, 42
Chapter 3 Set Theory and the Theory of Integration 55
3.1 Nowhere Dense Sets and their Measure
Theoretic Properties, 55
3.2 The Introduction of Outer Content, 61
3.3 Cantor s Development of the Theory of Sets
and its Application to the Theory of Inte¬
gration, 71
3.4 Curve Length and the Integral, 79
vii
viii contents
Chapter 4 The End of the Century: A Period of Transition 86
4.1 The Introduction of the Concept of Measur
ability, 86
4.2 Bokel s Theory of Measure, 97
4.3 schoenflies report on the theory of sets,
106
4.4 Researches on Term by Term Integration of
nonuniformly converging series, 110
Chapter 5 The Creation of Modern Integration Theory 120
5.1 Lebesgue s Theory of Integration, 120
5.2 The Work of Vitali and Young on Measure
and Integration, 146
5.3 Fubini s Theorem, 154
Chapter 6 Pioneering Applications of the Lebesgue
Integral 163
Epilogue The Lebesgue Stieltjes Integral 179
Appendix Dini s Theorem on the Differentiability of Con¬
tinuous Functions 197
Glossary 200
Special Symbols 204
List of Abbreviations 205
Bibliography 208
Index 225
|
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| callnumber-first | Q - Science |
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| classification_rvk | SK 430 |
| ctrlnum | (OCoLC)901151 (DE-599)BVBBV001968733 |
| dewey-full | 515/.43 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.43 |
| dewey-search | 515/.43 |
| dewey-sort | 3515 243 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV001968733 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:38:06Z |
| institution | BVB |
| isbn | 0828402825 |
| language | English |
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| physical | XV, 227 S. |
| publishDate | 1975 |
| publishDateSearch | 1975 |
| publishDateSort | 1975 |
| publisher | Chelsea |
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| spelling | Hawkins, Thomas 1938- Verfasser (DE-588)133470687 aut Lebesgue's theory of integration Its origins and development 2. ed. The Bronx, NY Chelsea 1975 XV, 227 S. txt rdacontent n rdamedia nc rdacarrier Intégrales généralisées Integrals, Generalized Integrationstheorie (DE-588)4138369-2 gnd rswk-swf Integration Mathematik (DE-588)4072852-3 gnd rswk-swf Lebesgue-Integral (DE-588)4034949-4 gnd rswk-swf Integrationstheorie (DE-588)4138369-2 s Lebesgue-Integral (DE-588)4034949-4 s DE-604 Integration Mathematik (DE-588)4072852-3 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=001283979&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 | Hawkins, Thomas 1938- Lebesgue's theory of integration Its origins and development Intégrales généralisées Integrals, Generalized Integrationstheorie (DE-588)4138369-2 gnd Integration Mathematik (DE-588)4072852-3 gnd Lebesgue-Integral (DE-588)4034949-4 gnd |
| subject_GND | (DE-588)4138369-2 (DE-588)4072852-3 (DE-588)4034949-4 |
| title | Lebesgue's theory of integration Its origins and development |
| title_auth | Lebesgue's theory of integration Its origins and development |
| title_exact_search | Lebesgue's theory of integration Its origins and development |
| title_full | Lebesgue's theory of integration Its origins and development |
| title_fullStr | Lebesgue's theory of integration Its origins and development |
| title_full_unstemmed | Lebesgue's theory of integration Its origins and development |
| title_short | Lebesgue's theory of integration |
| title_sort | lebesgue s theory of integration its origins and development |
| title_sub | Its origins and development |
| topic | Intégrales généralisées Integrals, Generalized Integrationstheorie (DE-588)4138369-2 gnd Integration Mathematik (DE-588)4072852-3 gnd Lebesgue-Integral (DE-588)4034949-4 gnd |
| topic_facet | Intégrales généralisées Integrals, Generalized Integrationstheorie Integration Mathematik Lebesgue-Integral |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001283979&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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