Theories of integration: the integrals of Riemann, Lebesgue, Henstock-Kurzweil, and McShane
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New Jersey [u.a.]
World Scientific
2004
|
| Schriftenreihe: | Series in real analysis
9 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | XIII, 268 S. graph. Darst. |
| ISBN: | 9812566112 9812388435 |
Internformat
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Datensatz im Suchindex
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| adam_text | SERIES IN REAL ANALYSIS - VOLUME 9 THEORIES OF INTEGRATION THE INTEGRALS
OF RIEMANN, LEBESGUE, HENSTOCK-KURZWEIL, AND MCSHANE DOUGLAS S KURTZ
CHARLES W SWARTZ NEW MEXICO STATE UNIVERSITY, USA JJP WORLD SCIENTIFIC
N E W J E R S E Y * L O N D O N * S I N G A P O R E * B E I J I N G * S
H A N G H A I * H O N G K O N G * T A I P E I * C H E N N A I CONTENTS
PREFACE VII 1. INTRODUCTION 1 1.1 AREAS 1 1.2 EXERCISES 9 2. RIEMANN
INTEGRAL 11 2.1 RIEMANN S DEFINITION 11 2.2 BASIC PROPERTIES 15 2.3
CAUCHY CRITERION 18 2.4 DARBOUX S DEFINITION 20 2.4.1 NECESSARY AND
SUFFICIENT CONDITIONS FOR DARBOUX INTE- GRABILITY 24 2.4.2 EQUIVALENCE
OF THE RIEMANN AND DARBOUX DEFINITIONS 25 2.4.3 LATTICE PROPERTIES 27
2.4.4 INTEGRABLE FUNCTIONS 30 2.4.5 ADDITIVITY OF THE INTEGRAL OVER
INTERVALS 31 2.5 FUNDAMENTAL THEOREM OF CALCULUS 33 2.5.1 INTEGRATION BY
PARTS AND SUBSTITUTION 37 2.6 CHARACTERIZATIONS OF INTEGRABILITY 38
2.6.1 LEBESGUE MEASURE ZERO 41 2.7 IMPROPER INTEGRALS 42 2.8 EXERCISES
46 3. CONVERGENCE THEOREMS AND THE LEBESGUE INTEGRAL 53 3.1 LEBESGUE S
DESCRIPTIVE DEFINITION OF THE INTEGRAL 56 XII THEORIES OF INTEGRATION
3.2 MEASURE 60 3.2.1 OUTER MEASURE 60 3.2.2 LEBESGUE MEASURE 64 3.2.3
THE CANTOR SET 78 3.3 LEBESGUE MEASURE IN R N 79 3.4 MEASURABLE
FUNCTIONS 85 3.5 LEBESGUE INTEGRAL 96 3.6 RIEMANN AND LEBESGUE INTEGRALS
ILL 3.7 MIKUSINSKI S CHARACTERIZATION OF THE LEBESGUE INTEGRAL . . . 113
3.8 FUBINI S THEOREM 117 3.9 THE SPACE OF LEBESGUE INTEGRABLE FUNCTIONS
122 3.10 EXERCISES 125 4. FUNDAMENTAL THEOREM OF CALCULUS AND THE
HENSTOCK- KURZWEIL INTEGRAL 133 4.1 DENJOY AND PERRON INTEGRALS 135 4.2
A GENERAL FUNDAMENTAL THEOREM OF CALCULUS 137 4.3 BASIC PROPERTIES 145
4.3.1 CAUCHY CRITERION 150 4.3.2 THE INTEGRAL AS A SET FUNCTION 151 4.4
UNBOUNDED INTERVALS 154 4.5 HENSTOCK S LEMMA 162 4.6 ABSOLUTE
INTEGRABILITY 172 4.6.1 BOUNDED VARIATION 172 4.6.2 ABSOLUTE
INTEGRABILITY AND INDEFINITE INTEGRALS . . . . 175 4.6.3 LATTICE
PROPERTIES 178 4.7 CONVERGENCE THEOREMS 180 4.8 HENSTOCK-KURZWEIL AND
LEBESGUE INTEGRALS 189 4.9 DIFFERENTIATING INDEFINITE INTEGRALS 190
4.9.1 FUNCTIONS WITH INTEGRAL 0 195 4.10 CHARACTERIZATIONS OF INDEFINITE
INTEGRALS 195 4.10.1 DERIVATIVES OF MONOTONE FUNCTIONS 198 4.10.2
INDEFINITE LEBESGUE INTEGRALS 203 4.10.3 INDEFINITE RIEMANN INTEGRALS
204 4.11 THE SPACE OF HENSTOCK-KURZWEIL INTEGRABLE FUNCTIONS .... 205
4.12 HENSTOCK-KURZWEIL INTEGRALS ON R N 206 4.13 EXERCISES 214 5.
ABSOLUTE INTEGRABILITY AND THE MCSHANE INTEGRAL 223 CONTENTS XIII 5.1
DEFINITIONS 224 5.2 BASIC PROPERTIES 227 5.3 ABSOLUTE INTEGRABILITY 229
5.3.1 FUNDAMENTAL THEOREM OF CALCULUS 232 5.4 CONVERGENCE THEOREMS 234
5.5 THE MCSHANE INTEGRAL AS A SET FUNCTION 240 5.6 THE SPACE OF MCSHANE
INTEGRABLE FUNCTIONS 244 5.7 MCSHANE, HENSTOCK-KURZWEIL AND LEBESGUE
INTEGRALS . . . . 245 5.8 MCSHANE INTEGRALS ONL 253 5.9 FUBINI AND
TONELLI THEOREMS 254 5.10 MCSHANE, HENSTOCK-KURZWEIL AND LEBESGUE
INTEGRALS IN M. N 257 5.11 EXERCISES 258 BIBLIOGRAPHY 263 INDEX 265
|
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| author | Kurtz, Douglas S. Swartz, Charles 1938- |
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| dewey-sort | 3515 243 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-09T20:00:04Z |
| institution | BVB |
| isbn | 9812566112 9812388435 |
| language | English |
| lccn | 2004049616 |
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| physical | XIII, 268 S. graph. Darst. |
| publishDate | 2004 |
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| publisher | World Scientific |
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| series | Series in real analysis |
| series2 | Series in real analysis |
| spelling | Kurtz, Douglas S. Verfasser aut Theories of integration the integrals of Riemann, Lebesgue, Henstock-Kurzweil, and McShane Douglas S. Kurtz ; Charles W. Swartz New Jersey [u.a.] World Scientific 2004 XIII, 268 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Series in real analysis 9 Integrales - Problemas, ejercicios, etc Intégrales aIntegrals Integrationstheorie (DE-588)4138369-2 gnd rswk-swf Integrationstheorie (DE-588)4138369-2 s DE-604 Swartz, Charles 1938- Verfasser (DE-588)131653601 aut Series in real analysis 9 (DE-604)BV001898092 9 http://www.gbv.de/du/services/agi/7FC532763C30621DC1256FDA0053C124/420000136757 Inhaltsverzeichnis HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012887821&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kurtz, Douglas S. Swartz, Charles 1938- Theories of integration the integrals of Riemann, Lebesgue, Henstock-Kurzweil, and McShane Series in real analysis Integrales - Problemas, ejercicios, etc Intégrales aIntegrals Integrationstheorie (DE-588)4138369-2 gnd |
| subject_GND | (DE-588)4138369-2 |
| title | Theories of integration the integrals of Riemann, Lebesgue, Henstock-Kurzweil, and McShane |
| title_auth | Theories of integration the integrals of Riemann, Lebesgue, Henstock-Kurzweil, and McShane |
| title_exact_search | Theories of integration the integrals of Riemann, Lebesgue, Henstock-Kurzweil, and McShane |
| title_full | Theories of integration the integrals of Riemann, Lebesgue, Henstock-Kurzweil, and McShane Douglas S. Kurtz ; Charles W. Swartz |
| title_fullStr | Theories of integration the integrals of Riemann, Lebesgue, Henstock-Kurzweil, and McShane Douglas S. Kurtz ; Charles W. Swartz |
| title_full_unstemmed | Theories of integration the integrals of Riemann, Lebesgue, Henstock-Kurzweil, and McShane Douglas S. Kurtz ; Charles W. Swartz |
| title_short | Theories of integration |
| title_sort | theories of integration the integrals of riemann lebesgue henstock kurzweil and mcshane |
| title_sub | the integrals of Riemann, Lebesgue, Henstock-Kurzweil, and McShane |
| topic | Integrales - Problemas, ejercicios, etc Intégrales aIntegrals Integrationstheorie (DE-588)4138369-2 gnd |
| topic_facet | Integrales - Problemas, ejercicios, etc Intégrales aIntegrals Integrationstheorie |
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