Topics in banach space integration:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey [u.a.]
World Scientific
2005
|
| Series: | Series in real analysis
10 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 298 S. |
| ISBN: | 9812564284 |
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Record in the Search Index
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| adam_text | SERIES IN REAL ANALYSIS - VOLUME 10 TOPICS IN BANACH SPACE INTEGRATION
STEFAN SCHWABIK CZECH ACADEMY OF SCIENCES, CZECH REPUBLIC YE GUOJU HOHAI
UNIVERSITY, CHINA WORLD SCIENTIFIC NEW JERSEY * LONDON * SINGAPORE *
BEIJING * SHANGHAI * HONG KONG * TAIPEI * CHENNAI CONTENTS PREFACE V
NOTATION IX 1. BOCHNER INTEGRAL 1 1.1 SIMPLE FUNCTIONS, MEASURABILITY 1
1.2 THE INTEGRAL OF SIMPLE FUNCTIONS 9 1.3 BOCHNER INTEGRAL 11 1.4
PROPERTIES OF BOCHNER INTEGRABLE FUNCTIONS AND OF THE BOCHNER INTEGRAL
22 2. DUNFORD AND PETTIS INTEGRALS 27 2.1 DUNFORD INTEGRAL ; 27 2.2
PETTIS INTEGRAL . 33 2.3 SOME PROPERTIES OF THE PETTIS INTEGRAL 36 3.
MCSHANE AND HENSTOCK-KURZWEIL INTEGRALS 45 3.1 SYSTEMS, PARTITIONS AND
GAUGES 45 3.2 DEFINITION OF THE MCSHANE AND HENSTOCK- KURZWEIL INTEGRALS
46 3.3 ELEMENTARY PROPERTIES OF THE MCSHANE AND HENSTOCK-KURZWEIL
INTEGRALS 48 3.4 THE SAKS-HENSTOCK LEMMA 55 3.5 A CONVERGENCE THEOREM 64
XI XII BANACH SPACE INTEGRATION 3.6 THE STRONG VERSIONS OF THE MCSHANE
AND HENSTOCK-KURZWEIL INTEGRALS 70 3.7 INTEGRATION OVER UNBOUNDED
INTERVALS AND SOME REMARKS 85 4. MORE ON THE MCSHANE INTEGRAL 87 4.1
SPECIAL PROPERTIES 87 4.2 AN EQUIVALENT DEFINITION OF THE MCSHANE
INTEGRAL . 113 4.3 ANOTHER CONVERGENCE THEOREM 119 5. COMPARISON OF THE
BOCHNER AND MCSHANE INTEGRALS 133 5.1 STRONG MCSHANE INTEGRABILITY AND
THE BOCHNER INTEGRAL 133 5.2 THE FINITE DIMENSIONAL CASE 150 5.3 THE
INFINITE DIMENSIONAL CASE 153 5.4 AN EXAMPLE 159 6. COMPARISON OF THE
PETTIS AND MCSHANE INTEGRALS 171 6.1 MCSHANE INTEGRABLE FUNCTIONS ARE
PETTIS INTEGRABLE 171 6.2 THE PROBLEM OF V C M 173 6.2.1 FUNCTIONS
WEAKLY EQUIVALENT TO MEASURABLE ONES 183 6.2.2 V C M DOES NOT HOLD IN
GENERAL ,_. 188 7. PRIMITIVE OF THE MCSHANE AND HENSTOCK- KURZWEIL
INTEGRALS 191 7.1 ABSOLUTELY CONTINUOUS FUNCTIONS AND FUNCTIONS OF
BOUNDED VARIATION 192 7.2 GENERALIZED ABSOLUTE CONTINUITY AND FUNCTIONS
OF GENERALIZED BOUNDED VARIATION 200 7.3 DIFFERENTIABILITY 202 7.4
PRIMITIVES 211 7.4.1 THE STRONG HENSTOCK-KURZWEIL INTEGRAL . . 212 7.4.2
THE MCSHANE AND THE STRONG MCSHANE INTEGRAL 218 CONTENTS XIII 7.4.3 THE
HENSTOCK-KURZWEIL INTEGRAL 223 7.5 VARIATIONAL MEASURES AND PRIMITIVES
FOR SM AND SHK, 226 7.6 CONTROLLED CONVERGENCE 231 8. GENERALIZATIONS OF
SOME INTEGRALS 251 8.1 BOCHNER INTEGRAL 251 8.2 DUNFORD AND PETTIS
INTEGRAL 254 8.2.1 DENJOY APPROACH 255 8.2.2 HENSTOCK-KURZWEIL APPROACH
269 8.2.3 SOME EXAMPLES 272 8.3 CONCLUDING REMARKS 273 APPENDIX A
CLASSICAL BANACH SPACES 277 A.I SPACES OF SEQUENCES 277 A.2 SPACES OF
FUNCTIONS 279 A.2.1 THE SPACES C(I) AND L P (I), 1 P OO . . 279
A.2.2 THE SPACES L X AND L^ 279 APPENDIX B SERIES IN BANACH SPACES 283
BIBLIOGRAPHY 291 INDEX 297
|
| adam_txt |
SERIES IN REAL ANALYSIS - VOLUME 10 TOPICS IN BANACH SPACE INTEGRATION
STEFAN SCHWABIK CZECH ACADEMY OF SCIENCES, CZECH REPUBLIC YE GUOJU HOHAI
UNIVERSITY, CHINA WORLD SCIENTIFIC NEW JERSEY * LONDON * SINGAPORE *
BEIJING * SHANGHAI * HONG KONG * TAIPEI * CHENNAI CONTENTS PREFACE V
NOTATION IX 1. BOCHNER INTEGRAL 1 1.1 SIMPLE FUNCTIONS, MEASURABILITY 1
1.2 THE INTEGRAL OF SIMPLE FUNCTIONS 9 1.3 BOCHNER INTEGRAL 11 1.4
PROPERTIES OF BOCHNER INTEGRABLE FUNCTIONS AND OF THE BOCHNER INTEGRAL
22 2. DUNFORD AND PETTIS INTEGRALS 27 2.1 DUNFORD INTEGRAL ; 27 2.2
PETTIS INTEGRAL . 33 2.3 SOME PROPERTIES OF THE PETTIS INTEGRAL 36 3.
MCSHANE AND HENSTOCK-KURZWEIL INTEGRALS 45 3.1 SYSTEMS, PARTITIONS AND
GAUGES 45 3.2 DEFINITION OF THE MCSHANE AND HENSTOCK- KURZWEIL INTEGRALS
46 3.3 ELEMENTARY PROPERTIES OF THE MCSHANE AND HENSTOCK-KURZWEIL
INTEGRALS 48 3.4 THE SAKS-HENSTOCK LEMMA 55 3.5 A CONVERGENCE THEOREM 64
XI XII BANACH SPACE INTEGRATION 3.6 THE STRONG VERSIONS OF THE MCSHANE
AND HENSTOCK-KURZWEIL INTEGRALS 70 3.7 INTEGRATION OVER UNBOUNDED
INTERVALS AND SOME REMARKS 85 4. MORE ON THE MCSHANE INTEGRAL 87 4.1
SPECIAL PROPERTIES 87 4.2 AN EQUIVALENT DEFINITION OF THE MCSHANE
INTEGRAL . 113 4.3 ANOTHER CONVERGENCE THEOREM 119 5. COMPARISON OF THE
BOCHNER AND MCSHANE INTEGRALS 133 5.1 STRONG MCSHANE INTEGRABILITY AND
THE BOCHNER INTEGRAL 133 5.2 THE FINITE DIMENSIONAL CASE 150 5.3 THE
INFINITE DIMENSIONAL CASE 153 5.4 AN EXAMPLE 159 6. COMPARISON OF THE
PETTIS AND MCSHANE INTEGRALS 171 6.1 MCSHANE INTEGRABLE FUNCTIONS ARE
PETTIS INTEGRABLE 171 6.2 THE PROBLEM OF V C M 173 6.2.1 FUNCTIONS
WEAKLY EQUIVALENT TO MEASURABLE ONES 183 6.2.2 V C M DOES NOT HOLD IN
GENERAL ,_. 188 7. PRIMITIVE OF THE MCSHANE AND HENSTOCK- KURZWEIL
INTEGRALS 191 7.1 ABSOLUTELY CONTINUOUS FUNCTIONS AND FUNCTIONS OF
BOUNDED VARIATION 192 7.2 GENERALIZED ABSOLUTE CONTINUITY AND FUNCTIONS
OF GENERALIZED BOUNDED VARIATION 200 7.3 DIFFERENTIABILITY 202 7.4
PRIMITIVES 211 7.4.1 THE STRONG HENSTOCK-KURZWEIL INTEGRAL . . 212 7.4.2
THE MCSHANE AND THE STRONG MCSHANE INTEGRAL 218 CONTENTS XIII 7.4.3 THE
HENSTOCK-KURZWEIL INTEGRAL 223 7.5 VARIATIONAL MEASURES AND PRIMITIVES
FOR SM AND SHK, 226 7.6 CONTROLLED CONVERGENCE 231 8. GENERALIZATIONS OF
SOME INTEGRALS 251 8.1 BOCHNER INTEGRAL 251 8.2 DUNFORD AND PETTIS
INTEGRAL 254 8.2.1 DENJOY APPROACH 255 8.2.2 HENSTOCK-KURZWEIL APPROACH
269 8.2.3 SOME EXAMPLES 272 8.3 CONCLUDING REMARKS 273 APPENDIX A
CLASSICAL BANACH SPACES 277 A.I SPACES OF SEQUENCES 277 A.2 SPACES OF
FUNCTIONS 279 A.2.1 THE SPACES C(I) AND L P (I), 1 P OO . . 279
A.2.2 THE SPACES L X AND L^ 279 APPENDIX B SERIES IN BANACH SPACES 283
BIBLIOGRAPHY 291 INDEX 297 |
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| index_date | 2024-07-02T14:00:16Z |
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| institution | BVB |
| isbn | 9812564284 |
| language | English |
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| physical | XIII, 298 S. |
| publishDate | 2005 |
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| publisher | World Scientific |
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| series | Series in real analysis |
| series2 | Series in real analysis |
| spelling | Schwabik, Štefan Verfasser aut Topics in banach space integration Stefan Schwabik ; Ye Guoju New Jersey [u.a.] World Scientific 2005 XIII, 298 S. txt rdacontent n rdamedia nc rdacarrier Series in real analysis 10 Espacios generalizados Espaços de banach larpcal Medida e integração larpcal Banach spaces Integrals Banach-Raum (DE-588)4004402-6 gnd rswk-swf Banach-Raum (DE-588)4004402-6 s DE-604 Guoju, Ye Verfasser aut Series in real analysis 10 (DE-604)BV001898092 10 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014646047&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schwabik, Štefan Guoju, Ye Topics in banach space integration Series in real analysis Espacios generalizados Espaços de banach larpcal Medida e integração larpcal Banach spaces Integrals Banach-Raum (DE-588)4004402-6 gnd |
| subject_GND | (DE-588)4004402-6 |
| title | Topics in banach space integration |
| title_auth | Topics in banach space integration |
| title_exact_search | Topics in banach space integration |
| title_exact_search_txtP | Topics in banach space integration |
| title_full | Topics in banach space integration Stefan Schwabik ; Ye Guoju |
| title_fullStr | Topics in banach space integration Stefan Schwabik ; Ye Guoju |
| title_full_unstemmed | Topics in banach space integration Stefan Schwabik ; Ye Guoju |
| title_short | Topics in banach space integration |
| title_sort | topics in banach space integration |
| topic | Espacios generalizados Espaços de banach larpcal Medida e integração larpcal Banach spaces Integrals Banach-Raum (DE-588)4004402-6 gnd |
| topic_facet | Espacios generalizados Espaços de banach Medida e integração Banach spaces Integrals Banach-Raum |
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