The theory of measures and integration:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Hoboken, NJ
Wiley-Interscience
2003
|
| Schriftenreihe: | Wiley series in probability and statistics
|
| Schlagworte: | |
| Online-Zugang: | Biographische Angaben Informationen des Verlegers Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | XVII, 594 S. |
| ISBN: | 0471249777 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804132832769998848 |
|---|---|
| adam_text | THE THEORY OF MEASURES AND INTEGRATION ERIC M. VESTRUP IWILEY-
INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION CONTENTS PREFACE
ACKNOWLEDGMENTS SET SYSTEMS 1.1 IR-SYSTEMS, -SYSTEMS, AND SEMIRINGS 1.2
FIELDS 1.3 CT-FIELDS 1.4 THE BOREL CT-FIELD 1.5 THE K-DIMENSIONAL BOREL
A-FIELD 1.6 A-FIELDS: CONSTRUCTION AND CARDINALITY 1.7 A CLASS OF
ETHEREAL BOREL SETS XI XVII 1 2 7 9 15 19 23 28 2 MEASURES 2.1 MEASURES
2.2 CONTINUITY OF MEASURES 2.3 A CLASS OF MEASURES 2.4 APPENDIX: PROOF
OF THE STIELTJES THEOREM 3 EXTENSIONS OF MEASURES 3.1 EXTENSIONS AND
RESTRICTIONS 3.2 OUTER MEASURES 3.3 CARATHEODORY S CRITERION 3.4
EXISTENCE OF EXTENSIONS 35 36 42 50 55 63 65 66 69 75 VIII CONTENTS 3.5
UNIQUENESS OF MEASURES AND EXTENSIONS 81 3.6 THE COMPLETION THEOREM 88
3.7 THE RELATIONSHIP BETWEEN V(A) AND :W(|X*) 93 3.8 APPROXIMATIONS 96
3.9 A FURTHER DESCRIPTION OF M( I*) 103 3.10 A CORRESPONDENCE THEOREM
105 4 LEBESGUE MEASURE 113 4.1 LEBESGUE MEASURE: EXISTENCE AND
UNIQUENESS 113 4.2 LEBESGUE SETS 116 4.3 TRANSLATION INVARIANCE OF
LEBESGUE MEASURE 124 4.4 LINEAR TRANSFORMATIONS 128 4.5 THE EXISTENCE OF
NON-LEBESGUE SETS 138 4.6 THE CANTOR SET AND THE LEBESGUE FUNCTION 143
4.7 A NON-BOREL LEBESGUE SET 151 4.8 THE IMPOSSIBILITY THEOREM 154 4.9
EXCURSUS: EXTREMELY NONMEASURABLE SETS 158 5 MEASURABLE FUNCTIONS 163
5.1 MEASURABILITY 165 5.2 COMBINING MEASURABLE FUNCTIONS 172 5.3
SEQUENCES OF MEASURABLE FUNCTIONS 178 5.4 ALMOST EVERYWHERE 182 5.5
SIMPLE FUNCTIONS 185 5.6 SOME CONVERGENCE CONCEPTS 188 5.7 CONTINUITY
AND MEASURABILITY 197 5.8 A GENERALIZED DEFINITION OF MEASURABILITY 206
6 THE LEBESGUE INTEGRAL 209 6.1 STAGE ONE: SIMPLE FUNCTIONS 210 6.2
STAGE TWO: NONNEGATIVE FUNCTIONS 216 6.3 STAGE THREE: GENERAL MEASURABLE
FUNCTIONS 233 6.4 STAGE FOUR: ALMOST EVERYWHERE DEFINED FUNCTIONS 248 7
INTEGRALS RELATIVE TO LEBESGUE MEASURE 267 7.1 SEMICONTINUITY 267 7.2
STEP FUNCTIONS IN EUCLIDEAN SPACE 273 7.3 THE RIEMANN INTEGRAL, PART ONE
277 7.4 THE RIEMANN INTEGRAL, PART TWO 281 7.5 CHANGE OF VARIABLES IN
THE LINEAR CASE 286 8 THE L.P SPACES 291 8.1 V SPACE: THE CASE 1 P
+ 295 8.2 THERIESZ*FISCHER THEOREM 300 8.3 LP SPACE: THE CASE 0 /?
1 306 CONTENTS IX 8.4 IP SPACE: THE CASE P = +00 8.5 CONTAINMENT
RELATIONS FOR IF SPACES 8.6 APPROXIMATION 8.7 MORE CONVERGENCE CONCEPTS
8.8 PRELUDE TO THE RIESZ REPRESENTATION THEOREM 8.9 THE RIESZ
REPRESENTATION THEOREM THE RADON-NIKODYM THEOREM 9.1 THE RADON-NIKODYM
THEOREM, PART I 9.2 THE RADON-NIKODYM THEOREM, PART II 9.3 FROM
RADON-NIKODYM TO RIESZ REPRESENTATION 9.4 MARTINGALE THEOREMS 10 11
PRODUCTS OF TWO MEASURE SPACES 10.1 PRODUCT MEASURES 10.2 THE FUBINI
THEOREMS 10.3 THE FUBINI THEOREMS IN EUCLIDEAN SPACE 10.4 THE
GENERALIZED MINKOWSKI INEQUALITY 10.5 CONVOLUTIONS 10.6 THE HARD
Y-LITTLEWOOD THEOREMS ARBITRARY PRODUCTS OF MEASURE SPACES 11.1 NOTATION
AND CONVENTIONS CONSTRUCTION OF THE PRODUCT MEASURE CONVERGENCE THEOREMS
IN PRODUCT SPACE THE L 2 STRONG LAW PRELUDE TO THE L L STRONG LAW THEZ,
1 STRONG LAW 11.2 11.3 11.4 11.5 11.6 REFERENCES INDEX 311 316 320 331
343 357 367 368 390 402 419 437 438 452 471 480 489 502 519 520 530 554
567 575 583 587 592
|
| any_adam_object | 1 |
| author | Vestrup, Eric M. |
| author_facet | Vestrup, Eric M. |
| author_role | aut |
| author_sort | Vestrup, Eric M. |
| author_variant | e m v em emv |
| building | Verbundindex |
| bvnumber | BV019386224 |
| callnumber-first | Q - Science |
| callnumber-label | QA325 |
| callnumber-raw | QA325 |
| callnumber-search | QA325 |
| callnumber-sort | QA 3325 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 430 |
| ctrlnum | (OCoLC)52288818 (DE-599)BVBBV019386224 |
| 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 |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:59:05Z |
| institution | BVB |
| isbn | 0471249777 |
| language | English |
| lccn | 2003053475 |
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| physical | XVII, 594 S. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Wiley-Interscience |
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| series2 | Wiley series in probability and statistics |
| spelling | Vestrup, Eric M. Verfasser aut The theory of measures and integration Eric M. Vestrup Measure theory and its applications Hoboken, NJ Wiley-Interscience 2003 XVII, 594 S. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics Integralen gtt Intégrales généralisées Maattheorie gtt Mesure, Théorie de la aMeasure theory aIntegrals, Generalized Integrationstheorie (DE-588)4138369-2 gnd rswk-swf Maßtheorie (DE-588)4074626-4 gnd rswk-swf Maßtheorie (DE-588)4074626-4 s DE-604 Integrationstheorie (DE-588)4138369-2 s http://www.loc.gov/catdir/bios/wiley044/2003053475.html Biographische Angaben http://www.loc.gov/catdir/description/wiley037/2003053475.html Informationen des Verlegers http://www.loc.gov/catdir/toc/wiley032/2003053475.html Inhaltsverzeichnis HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012849121&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Vestrup, Eric M. The theory of measures and integration Integralen gtt Intégrales généralisées Maattheorie gtt Mesure, Théorie de la aMeasure theory aIntegrals, Generalized Integrationstheorie (DE-588)4138369-2 gnd Maßtheorie (DE-588)4074626-4 gnd |
| subject_GND | (DE-588)4138369-2 (DE-588)4074626-4 |
| title | The theory of measures and integration |
| title_alt | Measure theory and its applications |
| title_auth | The theory of measures and integration |
| title_exact_search | The theory of measures and integration |
| title_full | The theory of measures and integration Eric M. Vestrup |
| title_fullStr | The theory of measures and integration Eric M. Vestrup |
| title_full_unstemmed | The theory of measures and integration Eric M. Vestrup |
| title_short | The theory of measures and integration |
| title_sort | the theory of measures and integration |
| topic | Integralen gtt Intégrales généralisées Maattheorie gtt Mesure, Théorie de la aMeasure theory aIntegrals, Generalized Integrationstheorie (DE-588)4138369-2 gnd Maßtheorie (DE-588)4074626-4 gnd |
| topic_facet | Integralen Intégrales généralisées Maattheorie Mesure, Théorie de la aMeasure theory aIntegrals, Generalized Integrationstheorie Maßtheorie |
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