Introduction to gauge integrals:
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Singapore
World Scientific
© 2001
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| Subjects: | |
| Online Access: | FAW01 FAW02 Volltext |
| Item Description: | Includes bibliographical references (pages 149-153) and index 1. Introduction to the gauge or Henstock-Kurzweil integral -- 2. Basic properties of the gauge integral -- 3. Henstock's lemma and improper integrals -- 4. The gauge integral over unbounded intervals -- 5. Convergence theorems -- 6. Integration over more general sets: Lebesgue measure -- 7. The space of gauge integrable functions -- 8. Multiple integrals and Fubini's theorem -- 9. The McShane integral. 9.1. Definition and basic properties. 9.2. Convergence theorems. 9.3. Integrability of products and integration by parts. 9.4. More general convergence theorems. 9.5. The space of McShane integrable functions. 9.6. Multiple integrals and Fubini's theorem -- 10. McShane integrability is equivalent to absolute Henstock-Kurzweil integrability This book presents the Henstock/Kurzweil integral and the McShane integral. These two integrals are obtained by changing slightly the definition of the Riemann integral. These variations lead to integrals which are much more powerful than the Riemann integral. The Henstock/Kurzweil integral is an unconditional integral for which the fundamental theorem of calculus holds in full generality, while the McShane integral is equivalent to the Lebesgue integral in Euclidean spaces. A basic knowledge of introductory real analysis is required of the reader, who should be familiar with the fundamental properties of the real numbers, convergence, series, differentiation, continuity, etc |
| Physical Description: | 1 Online-Ressource (x, 157 pages) |
| ISBN: | 1281956317 9781281956316 9789810242398 9789812810656 9810242395 981281065X |
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MARC
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| 245 | 1 | 0 | |a Introduction to gauge integrals |c Charles Swartz |
| 246 | 1 | 3 | |a Gauge integrals |
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| 500 | |a Includes bibliographical references (pages 149-153) and index | ||
| 500 | |a 1. Introduction to the gauge or Henstock-Kurzweil integral -- 2. Basic properties of the gauge integral -- 3. Henstock's lemma and improper integrals -- 4. The gauge integral over unbounded intervals -- 5. Convergence theorems -- 6. Integration over more general sets: Lebesgue measure -- 7. The space of gauge integrable functions -- 8. Multiple integrals and Fubini's theorem -- 9. The McShane integral. 9.1. Definition and basic properties. 9.2. Convergence theorems. 9.3. Integrability of products and integration by parts. 9.4. More general convergence theorems. 9.5. The space of McShane integrable functions. 9.6. Multiple integrals and Fubini's theorem -- 10. McShane integrability is equivalent to absolute Henstock-Kurzweil integrability | ||
| 500 | |a This book presents the Henstock/Kurzweil integral and the McShane integral. These two integrals are obtained by changing slightly the definition of the Riemann integral. These variations lead to integrals which are much more powerful than the Riemann integral. The Henstock/Kurzweil integral is an unconditional integral for which the fundamental theorem of calculus holds in full generality, while the McShane integral is equivalent to the Lebesgue integral in Euclidean spaces. A basic knowledge of introductory real analysis is required of the reader, who should be familiar with the fundamental properties of the real numbers, convergence, series, differentiation, continuity, etc | ||
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Record in the Search Index
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| author | Swartz, Charles 1938- |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| id | DE-604.BV043090407 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:17:07Z |
| institution | BVB |
| isbn | 1281956317 9781281956316 9789810242398 9789812810656 9810242395 981281065X |
| language | English |
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| oclc_num | 268993106 |
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| owner | DE-1046 DE-1047 |
| owner_facet | DE-1046 DE-1047 |
| physical | 1 Online-Ressource (x, 157 pages) |
| psigel | ZDB-4-EBA ZDB-4-EBA FAW_PDA_EBA |
| publishDate | 2001 |
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| publisher | World Scientific |
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| spelling | Swartz, Charles 1938- Verfasser (DE-588)131653601 aut Introduction to gauge integrals Charles Swartz Gauge integrals Singapore World Scientific © 2001 1 Online-Ressource (x, 157 pages) txt rdacontent c rdamedia cr rdacarrier Includes bibliographical references (pages 149-153) and index 1. Introduction to the gauge or Henstock-Kurzweil integral -- 2. Basic properties of the gauge integral -- 3. Henstock's lemma and improper integrals -- 4. The gauge integral over unbounded intervals -- 5. Convergence theorems -- 6. Integration over more general sets: Lebesgue measure -- 7. The space of gauge integrable functions -- 8. Multiple integrals and Fubini's theorem -- 9. The McShane integral. 9.1. Definition and basic properties. 9.2. Convergence theorems. 9.3. Integrability of products and integration by parts. 9.4. More general convergence theorems. 9.5. The space of McShane integrable functions. 9.6. Multiple integrals and Fubini's theorem -- 10. McShane integrability is equivalent to absolute Henstock-Kurzweil integrability This book presents the Henstock/Kurzweil integral and the McShane integral. These two integrals are obtained by changing slightly the definition of the Riemann integral. These variations lead to integrals which are much more powerful than the Riemann integral. The Henstock/Kurzweil integral is an unconditional integral for which the fundamental theorem of calculus holds in full generality, while the McShane integral is equivalent to the Lebesgue integral in Euclidean spaces. A basic knowledge of introductory real analysis is required of the reader, who should be familiar with the fundamental properties of the real numbers, convergence, series, differentiation, continuity, etc Kurzweil-Henstock, Intégrale de McShane, Intégrale de MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh Henstock-Kurzweil integral fast McShane integral fast Henstock-Kurzweil integral McShane integral Henstock-Integration (DE-588)4159545-2 gnd rswk-swf Riemannsches Integral (DE-588)4049996-0 gnd rswk-swf Riemannsches Integral (DE-588)4049996-0 s 1\p DE-604 Henstock-Integration (DE-588)4159545-2 s 2\p DE-604 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=235917 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Swartz, Charles 1938- Introduction to gauge integrals Kurzweil-Henstock, Intégrale de McShane, Intégrale de MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh Henstock-Kurzweil integral fast McShane integral fast Henstock-Kurzweil integral McShane integral Henstock-Integration (DE-588)4159545-2 gnd Riemannsches Integral (DE-588)4049996-0 gnd |
| subject_GND | (DE-588)4159545-2 (DE-588)4049996-0 |
| title | Introduction to gauge integrals |
| title_alt | Gauge integrals |
| title_auth | Introduction to gauge integrals |
| title_exact_search | Introduction to gauge integrals |
| title_full | Introduction to gauge integrals Charles Swartz |
| title_fullStr | Introduction to gauge integrals Charles Swartz |
| title_full_unstemmed | Introduction to gauge integrals Charles Swartz |
| title_short | Introduction to gauge integrals |
| title_sort | introduction to gauge integrals |
| topic | Kurzweil-Henstock, Intégrale de McShane, Intégrale de MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh Henstock-Kurzweil integral fast McShane integral fast Henstock-Kurzweil integral McShane integral Henstock-Integration (DE-588)4159545-2 gnd Riemannsches Integral (DE-588)4049996-0 gnd |
| topic_facet | Kurzweil-Henstock, Intégrale de McShane, Intégrale de MATHEMATICS / Calculus MATHEMATICS / Mathematical Analysis Henstock-Kurzweil integral McShane integral Henstock-Integration Riemannsches Integral |
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