Real variable and integration: with historical notes
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Stuttgart
Teubner
1976
|
| Edition: | 1. Aufl. |
| Series: | Mathematische Leitfäden
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 278 S. |
| ISBN: | 3519022095 |
Staff View
MARC
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| 100 | 1 | |a Benedetto, John J. |d 1939- |e Verfasser |0 (DE-588)132081482 |4 aut | |
| 245 | 1 | 0 | |a Real variable and integration |b with historical notes |c by John J. Benedetto |
| 250 | |a 1. Aufl. | ||
| 264 | 1 | |a Stuttgart |b Teubner |c 1976 | |
| 300 | |a 278 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a Mathematische Leitfäden | |
| 650 | 4 | |a Fonctions de variables réelles | |
| 650 | 4 | |a Intégrales généralisées | |
| 650 | 4 | |a Mesure, Théorie de la | |
| 650 | 4 | |a Functions of real variables | |
| 650 | 4 | |a Integrals, Generalized | |
| 650 | 4 | |a Measure theory | |
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| 650 | 0 | 7 | |a Lebesgue-Integral |0 (DE-588)4034949-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Radon-Nikodymscher Satz |0 (DE-588)4176848-6 |2 gnd |9 rswk-swf |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-004002601 | ||
Record in the Search Index
| DE-BY-862_location | 2000 |
|---|---|
| DE-BY-FWS_call_number | 2000/SK 430 B462 |
| DE-BY-FWS_katkey | 117083 |
| DE-BY-FWS_media_number | 083000028318 |
| _version_ | 1824555436299255809 |
| adam_text | Table of contents
1 Classical real variable
1.1 Set theory—a framework 13
1.2 The topology of R 13
1.3 Classical real variable—motivation for the Lebesgue theory 19
1.3.1 Continuous functions 21
1.3.2 Sets of differentiability 26
1.4 References for the history of integration theory 31
Problems 32
2 Lebesgue measure and general measure theory
2.1 The theory of measure prior to Lebesgue, and preliminaries 38
2.2 The existence of Lebesgue measure 43
2.3 General measure theory 51
2.4 Approximation theorems for measurable functions 58
Problems 64
3 The Lebesgue integral
3.1 Motivation 72
3.2 The Lebesgue integral 75
3.3 The Lebesgue dominated convergence theorem 82
3.4 The Riemann and Lebesgue integrals 92
3.5 Some fundamental applications 98
Problems 101
A 3.1 Sets of uniqueness and measure zero 113
4 The relationship between differentiation and integration on R
4.1 Functions of bounded variation and associated measures 118
4.2 Decomposition into discrete and continuous parts 126
4.3 The Lebesgue differentiation theorem 132
4.4 FTC I 138
4.5 Absolute continuity and FTC II 143
4.6 Absolutely continuous functions 146
Problems 151
Table of contents 9
5 Spaces of measures and the Radon Nikodym theorem
5.1 Signed and complex measures, and the basic decomposition theorems 163
5.2 Discrete and continuous, absolutely continuous and singular measures .... 174
5.3 The Vitali Lebesgue Radon Nikodym theorem 180
5.4 The relation between set and point functions 187
5.5 LPK(X), 1 =£ p « oo 192
Problems 198
A 5.1 The Radon Nikodym theorem: historical notes on Lusin s problem and
Vitali 208
6 Weak convergence of measures
6.1 Vitali s theorems 211
6.2 The Nikodym and Hahn Saks theorems 216
6.3 Weak convergence of measures 224
A 6.1 Vitali 229
Appendices
I Metric spaces and Banach spaces
1.1 Definitions of spaces 230
1.2 Examples 232
1.3 Separability 235
1.4 Moore Smith and Arzela Ascoli theorems 236
1.5 Uniformly continuous functions 238
1.6 Baire category theorem 239
1.7 Uniform boundedness principle 242
1.8 Hahn Banach theorem 244
1.9 The weak and weak * topologies 246
1.10 Linear maps 249
II Fubini s theorem
m The Riesz representation theorem (RRT)
111.1 Riesz s representation theorem 255
111.2 RRT 257
111.3 Radon measures 258
111.4 Radon measures and countably additive set functions 260
111.5 Support and the approximation theorem 262
111.6 Haar measure 263
Bibliography 267
Index of proper names 272
Index of terms 275
|
| any_adam_object | 1 |
| author | Benedetto, John J. 1939- |
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| 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 | 1. Aufl. |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2025-02-20T07:07:38Z |
| institution | BVB |
| isbn | 3519022095 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-004002601 |
| oclc_num | 2430927 |
| open_access_boolean | |
| owner | DE-739 DE-29T DE-N2 DE-91G DE-BY-TUM DE-384 DE-703 DE-355 DE-BY-UBR DE-20 DE-862 DE-BY-FWS DE-824 DE-19 DE-BY-UBM DE-634 DE-83 DE-11 DE-188 DE-706 |
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| physical | 278 S. |
| publishDate | 1976 |
| publishDateSearch | 1976 |
| publishDateSort | 1976 |
| publisher | Teubner |
| record_format | marc |
| series2 | Mathematische Leitfäden |
| spellingShingle | Benedetto, John J. 1939- Real variable and integration with historical notes Fonctions de variables réelles Intégrales généralisées Mesure, Théorie de la Functions of real variables Integrals, Generalized Measure theory Integration Mathematik (DE-588)4072852-3 gnd Lebesgue-Integral (DE-588)4034949-4 gnd Radon-Nikodymscher Satz (DE-588)4176848-6 gnd |
| subject_GND | (DE-588)4072852-3 (DE-588)4034949-4 (DE-588)4176848-6 |
| title | Real variable and integration with historical notes |
| title_auth | Real variable and integration with historical notes |
| title_exact_search | Real variable and integration with historical notes |
| title_full | Real variable and integration with historical notes by John J. Benedetto |
| title_fullStr | Real variable and integration with historical notes by John J. Benedetto |
| title_full_unstemmed | Real variable and integration with historical notes by John J. Benedetto |
| title_short | Real variable and integration |
| title_sort | real variable and integration with historical notes |
| title_sub | with historical notes |
| topic | Fonctions de variables réelles Intégrales généralisées Mesure, Théorie de la Functions of real variables Integrals, Generalized Measure theory Integration Mathematik (DE-588)4072852-3 gnd Lebesgue-Integral (DE-588)4034949-4 gnd Radon-Nikodymscher Satz (DE-588)4176848-6 gnd |
| topic_facet | Fonctions de variables réelles Intégrales généralisées Mesure, Théorie de la Functions of real variables Integrals, Generalized Measure theory Integration Mathematik Lebesgue-Integral Radon-Nikodymscher Satz |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004002601&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT benedettojohnj realvariableandintegrationwithhistoricalnotes |
Indexes
THWS Schweinfurt Zentralbibliothek Lesesaal
| Call Number: |
2000 SK 430 B462 |
|---|---|
| Copy 1 | ausleihbar Available Place a Hold |