Lebesgue measure and integral:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Pitman
1982
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 221 S. |
| ISBN: | 0273017543 |
Internformat
MARC
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
PREFACE v
CHAPTER 1 SETS OF POINTS 1
1.1 Introduction 1
1.2 Euclidean rc space and vector spaces 3
1.3 Sets of points 5
1.4 Topological ideas 10
1.5 Countable sets 13
1.6 Cartesian products 15
* 1.7 Proof of Heine Borel Covering Theorem 16
CHAPTER 2 RIEMANN INTEGRAL 18
2.1 Introduction 18
2.2 Intervals and step functions 20
2.3 Integral of a step function 22
2.4 Integral of a bounded function 24
2.5 Evaluation of integrals 32
2.6 Improper integrals 35
2.7 Repeated integrals 39
2.8 Change of variable 43
2.9 Limiting properties of the integral 45
* 2.10 Stieltjes integral 47
* 2.11 Contour integration 49
* 2.12 Relation to the Riemann and Darboux definitions of 51
the integral
2.13 Evaluation of the conditionally convergent integral 54
f *â„¢ sin x ,
dx
Jo x
CHAPTER 3 LEBESGUE MEASURE 56
3.1 Introduction 56
3.2 Rings and premeasures 58
3.3 Outer measure and measurability 61
3.4 Expanding and contracting sequences 71
3.5 Some examples of measure calculations 73
3.6 Extending the application of the theory 77
3.7 Measurable functions 79
viii
* 3.8 Premeasure properties 84
* 3.9 Egoroff s theorem 88
CHAPTER 4 LEBESGUE INTEGRAL 90
4.1 Introduction and definitions 90
4.2 Basic properties of the integral 93
4.3 Vector space interpretation of the integral 101
4.4 Limiting properties of the integral 109
4.5 Fubini s theorem 119
4.6 Some examples and further exercises 125
* 4.7 Relations between definitions of the integral 128
CHAPTER 5 DIFFERENTIABILITY PROPERTIES 131
OF THE INTEGRAL
5.1 Introduction: Dense subsets and mean continuity 131
5.2 Functions of bounded variation and absolutely 139
continuous functions
5.3 Monotone functions 144
5.4 Differentiating an integral 149
5.5 Integrating a derivative 152
5.6 Types of convergence 156
5.7 Second mean value theorem 161
* 5.8 Contraction mapping theorem 163
CHAPTER 6 INTEGRALS AND SET FUNCTIONS 166
6.1 Signed measures 166
6.2 Linear maps between Euclidean spaces 174
6.3 Differentiation of a set function 178
6.4 Change of variable theorem 183
CHAPTER 7 MORE GENERAL INTEGRALS 187
7.1 Introduction 187
7.2 Application of measure theory to probability 188
* 7.3 The Kolmogorov extension theorem for measures 195
* 7.4 The Bochner integral 199
* 7.5 Vector measures 207
* 7.6 Wiener measure and Brownian motion 210
BIBLIOGRAPHY 215
INDEX 217
ix
|
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| classification_rvk | SK 430 |
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| ctrlnum | (OCoLC)612053763 (DE-599)BVBBV002295342 |
| discipline | Mathematik |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:43:33Z |
| institution | BVB |
| isbn | 0273017543 |
| language | English |
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| physical | IX, 221 S. |
| publishDate | 1982 |
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| spelling | Craven, Bruce D. Verfasser aut Lebesgue measure and integral Boston, MA Pitman 1982 IX, 221 S. txt rdacontent n rdamedia nc rdacarrier Lebesgue-Maß (DE-588)4240914-7 gnd rswk-swf Lebesgue-Integral (DE-588)4034949-4 gnd rswk-swf Maßtheorie (DE-588)4074626-4 gnd rswk-swf Lebesgue-Integral (DE-588)4034949-4 s Maßtheorie (DE-588)4074626-4 s DE-604 Lebesgue-Maß (DE-588)4240914-7 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=001508454&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 | Craven, Bruce D. Lebesgue measure and integral Lebesgue-Maß (DE-588)4240914-7 gnd Lebesgue-Integral (DE-588)4034949-4 gnd Maßtheorie (DE-588)4074626-4 gnd |
| subject_GND | (DE-588)4240914-7 (DE-588)4034949-4 (DE-588)4074626-4 |
| title | Lebesgue measure and integral |
| title_auth | Lebesgue measure and integral |
| title_exact_search | Lebesgue measure and integral |
| title_full | Lebesgue measure and integral |
| title_fullStr | Lebesgue measure and integral |
| title_full_unstemmed | Lebesgue measure and integral |
| title_short | Lebesgue measure and integral |
| title_sort | lebesgue measure and integral |
| topic | Lebesgue-Maß (DE-588)4240914-7 gnd Lebesgue-Integral (DE-588)4034949-4 gnd Maßtheorie (DE-588)4074626-4 gnd |
| topic_facet | Lebesgue-Maß Lebesgue-Integral Maßtheorie |
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