Measure and integration:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Reading, MA u.a.
Reading, MA u.a.
1971
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804128278869442560 |
|---|---|
| adam_text | CONTENTS
Chapter 1 Background
1 Sets and functions 1
2 Algebra of sets 5
3 Cardinal numbers 9
4 Pseudo-metric spaces 11
5 Limits and continuity 15
6 Uniform limits 16
7 Function spaces 19
8 General topology 21
Chapter 2 Measure—General Theory
9 Additive classes and Borel sets 25
10 Additive set functions 31
11 Outer measures 42
12 Regular outer measures 50
13 Metric outer measures 57
Chapter 3 Measure—Specific Examples
14 Lebesgue-Stieltjes measures 68
*15 Probability 78
*16 Hausdorff measures 83
* 17 Haar measure 86
18 Nonmeasurable sets 93
Chapter 4 Measurable Functions
19 Definitions and basic properties 97
20 Operations on measurable functions 102
21 Approximation theorems 106
*22 Random variables 112
Chapter 5 Integration
23 The integral of a simple function 116
24 Integrable functions 120
25 Elementary properties of the integral 127
26 Additivity of the integral 132
27 Absolute continuity 136
28 Dominated convergence 145
xi
Xii CONTENTS
29 Fubini s theorem 149
*30 Expectation of a random variable 158
Chapter 6 Differentiation
31 Summary of the problem 167
32 Vitali coverings 171
33 Differentiation of additive set functions 176
34 The Lebesgue decomposition 180
*35 Metric density and approximate continuity 184
*36 Differentiation with respect to nets 191
Chapter 7 Convergence Theorems
37 Uniform and almost everywhere convergence 199
38 Convergence in measure and in mean 200
39 Relations among convergence types 206
40 Convergence of measures and integrals 208
41 The Lp spaces 215
42 Cauchy theorems 220
*43 Orthogonal expansions in Hilbert space 224
Chapter 8 Functional Analysis
44 Banach spaces 232
45 The Hahn-Banach theorem 238
46 Representation of linear functionals 245
47 Hamel bases 254
48 Weak and weak* sequential convergence 257
49 Weak* topologies 262
50 The closed-graph theorem 268
Bibliography 279
Index of postulates 281
Index of symbols 283
Subject index 287
|
| any_adam_object | 1 |
| author | Munroe, Marshall Evans |
| author_facet | Munroe, Marshall Evans |
| author_role | aut |
| author_sort | Munroe, Marshall Evans |
| author_variant | m e m me mem |
| building | Verbundindex |
| bvnumber | BV013488767 |
| classification_rvk | SK 430 |
| ctrlnum | (OCoLC)467133442 (DE-599)BVBBV013488767 |
| dewey-full | 515.42 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 .42 |
| dewey-search | 515 .42 |
| dewey-sort | 3515 242 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:46:43Z |
| institution | BVB |
| language | English |
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| publishDate | 1971 |
| publishDateSearch | 1971 |
| publishDateSort | 1971 |
| publisher | Reading, MA u.a. |
| record_format | marc |
| spelling | Munroe, Marshall Evans Verfasser aut Measure and integration 2. ed. Reading, MA u.a. Reading, MA u.a. 1971 txt rdacontent n rdamedia nc rdacarrier Integration Mathematik (DE-588)4072852-3 gnd rswk-swf Maßtheorie (DE-588)4074626-4 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Integrationstheorie (DE-588)4138369-2 gnd rswk-swf Maß Mathematik (DE-588)4037856-1 gnd rswk-swf Maß Mathematik (DE-588)4037856-1 s DE-604 Integration Mathematik (DE-588)4072852-3 s Maßtheorie (DE-588)4074626-4 s Integrationstheorie (DE-588)4138369-2 s Funktionalanalysis (DE-588)4018916-8 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=009205798&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 | Munroe, Marshall Evans Measure and integration Integration Mathematik (DE-588)4072852-3 gnd Maßtheorie (DE-588)4074626-4 gnd Funktionalanalysis (DE-588)4018916-8 gnd Integrationstheorie (DE-588)4138369-2 gnd Maß Mathematik (DE-588)4037856-1 gnd |
| subject_GND | (DE-588)4072852-3 (DE-588)4074626-4 (DE-588)4018916-8 (DE-588)4138369-2 (DE-588)4037856-1 |
| title | Measure and integration |
| title_auth | Measure and integration |
| title_exact_search | Measure and integration |
| title_full | Measure and integration |
| title_fullStr | Measure and integration |
| title_full_unstemmed | Measure and integration |
| title_short | Measure and integration |
| title_sort | measure and integration |
| topic | Integration Mathematik (DE-588)4072852-3 gnd Maßtheorie (DE-588)4074626-4 gnd Funktionalanalysis (DE-588)4018916-8 gnd Integrationstheorie (DE-588)4138369-2 gnd Maß Mathematik (DE-588)4037856-1 gnd |
| topic_facet | Integration Mathematik Maßtheorie Funktionalanalysis Integrationstheorie Maß Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009205798&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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