The Lebesgue-Stieltjes integral: a practical introduction
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
2000
|
| Series: | Undergraduate texts in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 228 S. graph. Darst. |
| ISBN: | 0387950125 |
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Record in the Search Index
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| adam_text | M. CARTER B. VAN BRUNT THE LEBESGUE- STIELTJES INTEGRAL A PRACTICAL
INTRODUCTION WITH 45 ILLUSTRATIONS SPRINGER CONTENTS PREFACE V 1 REAL
NUMBERS 1 1.1 RATIONAL AND IRRATIONAL NUMBERS 1 1.2 THE EXTENDED REAL
NUMBER SYSTEM 6 1.3 BOUNDS 8 2 SOME ANALYTIC PRELIMINARIES 11 2.1
MONOTONE SEQUENCES 11 2.2 DOUBLE SERIES 13 2.3 ONE-SIDED LIMITS 16 2.4
MONOTONE FUNCTIONS 20 2.5 STEP FUNCTIONS 24 2.6 POSITIVE AND NEGATIVE
PARTS OF A FUNCTION 28 2.7 BOUNDED VARIATION AND ABSOLUTE CONTINUITY 29
3 THE RIEMANN INTEGRAL 39 3.1 DEFINITION OF THE INTEGRAL 39 3.2 IMPROPER
INTEGRALS 44 3.3 A NONINTEGRABLE FUNCTION 46 VII VLLL CONTENTS 4 THE
LEBESGUE-STIELTJES INTEGRAL 49 4.1 THE MEASURE OF AN INTERVAL 49 4.2
PROBABILITY MEASURES 52 4.3 SIMPLE SETS 55 4.4 STEP FUNCTIONS REVISITED
56 4.5 DEFINITION OF THE INTEGRAL 60 4.6 THE LEBESGUE INTEGRAL 67 5
PROPERTIES OF THE INTEGRAL 71 5.1 BASIC PROPERTIES 71 5.2 NULL FUNCTIONS
AND NULL SETS 75 5.3 CONVERGENCE THEOREMS 79 5.4 EXTENSIONS OF THE
THEORY 81 6 INTEGRAL CALCULUS 87 6.1 EVALUATION OF INTEGRALS 87 6.2 TWO
THEOREMS OF INTEGRAL CALCULUS 97 6.3 INTEGRATION AND DIFFERENTIATION 102
7 DOUBLE AND REPEATED INTEGRALS 113 7.1 MEASURE OF A RECTANGLE 113 7.2
SIMPLE SETS AND SIMPLE FUNCTIONS IN TWO DIMENSIONS 114 7.3 THE
LEBESGUE-STIELTJES DOUBLE INTEGRAL 115 7.4 REPEATED INTEGRALS AND
FUBINI S THEOREM 115 8 THE LEBESGUE SPACES IF 123 8.1 NORMED SPACES 124
8.2 BANACH SPACES 131 8.3 COMPLETION OF SPACES 135 8.4 THE SPACE L 1 138
8.5 THE LEBESGUE IP 142 8.6 SEPARABLE SPACES 150 8.7 COMPLEX 1/SPACES
152 8.8 THE HARDY SPACES H P 154 8.9 SOBOLEV SPACES W^ P 161 CONTENTS IX
9 HILBERT SPACES AND L 2 165 9.1 HILBERT SPACES 165 9.2 ORTHOGONAL SETS
172 9.3 CLASSICAL FOURIER SERIES 180 9.4 THE STURM-LIOUVILLE PROBLEM 188
9.5 OTHER BASES FOR L 2 199 10 EPILOGUE 203 10.1 GENERALIZATIONS OF THE
LEBESGUE INTEGRAL 203 10.2 RIEMANN STRIKES BACK 205 10.3 FURTHER READING
207 APPENDIX: HINTS AND ANSWERS TO SELECTED EXERCISES 209 REFERENCES 221
INDEX 225
|
| any_adam_object | 1 |
| author | Carter, Michael Van Brunt, Bruce |
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| dewey-sort | 3515 243 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:42:30Z |
| institution | BVB |
| isbn | 0387950125 |
| language | English |
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| physical | IX, 228 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Springer |
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| series2 | Undergraduate texts in mathematics |
| spelling | Carter, Michael Verfasser aut The Lebesgue-Stieltjes integral a practical introduction M. Carter ; B. van Brunt New York [u.a.] Springer 2000 IX, 228 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Undergraduate texts in mathematics Lebesgue, Intégrale de Lebesgue, Intégrale de ram Lebesgue integral Lebesgue-Stieltjes-Integral (DE-588)4304016-0 gnd rswk-swf Lebesgue-Stieltjes-Integral (DE-588)4304016-0 s DE-604 Van Brunt, Bruce Verfasser (DE-588)122257499 aut HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009032019&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Carter, Michael Van Brunt, Bruce The Lebesgue-Stieltjes integral a practical introduction Lebesgue, Intégrale de Lebesgue, Intégrale de ram Lebesgue integral Lebesgue-Stieltjes-Integral (DE-588)4304016-0 gnd |
| subject_GND | (DE-588)4304016-0 |
| title | The Lebesgue-Stieltjes integral a practical introduction |
| title_auth | The Lebesgue-Stieltjes integral a practical introduction |
| title_exact_search | The Lebesgue-Stieltjes integral a practical introduction |
| title_full | The Lebesgue-Stieltjes integral a practical introduction M. Carter ; B. van Brunt |
| title_fullStr | The Lebesgue-Stieltjes integral a practical introduction M. Carter ; B. van Brunt |
| title_full_unstemmed | The Lebesgue-Stieltjes integral a practical introduction M. Carter ; B. van Brunt |
| title_short | The Lebesgue-Stieltjes integral |
| title_sort | the lebesgue stieltjes integral a practical introduction |
| title_sub | a practical introduction |
| topic | Lebesgue, Intégrale de Lebesgue, Intégrale de ram Lebesgue integral Lebesgue-Stieltjes-Integral (DE-588)4304016-0 gnd |
| topic_facet | Lebesgue, Intégrale de Lebesgue integral Lebesgue-Stieltjes-Integral |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009032019&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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