Real analysis: modern techniques and their applications
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
Wiley
[1999]
|
| Ausgabe: | Second edition |
| Schriftenreihe: | Pure and applied mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xiv, 386 Seiten Illustrationen |
| ISBN: | 9780471317166 |
Internformat
MARC
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Datensatz im Suchindex
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| adam_text |
REAL ANALYSIS MODERN TECHNIQUES AND THEIR APPLICATIONS SECOND EDITION
GERALD B. FOUAND A WILEY-INTERSCIENCE PUBLICATION JOHN WILEY& SONS, INC.
NEW YORK / CHICHESTER / WEINHEIM / BRISBANE / SINGAPORE / TORONTO K
CONTENTS PREFACE PROLOGUE 0.1 THE LANGUAGE OFSET THEORY 0.2 ORDERINGS
0.3 CARDINALITY 0.4 MORE ABOUT WELL ORDERED SETS 0.5 THE EXTENDED REAL
NUMBER SYSTEM 0.6 METRIE SPACES 0.7 NOTES AND REFERENCES MEASURES 1.1
INTRODUCTION 1.2 A-ALGEBRAS 1.3 MEASURES 1.4 OUTER MEASURES 1.5 BOREL
MEASURES ON THE REAL LINE 1.6 NOTES AND REFERENCES VII 1 1 4 6 9 10 13
16 19 19 21 24 28 33 40 XI XUE CONTENTS INTEGRATION 2.1 2.2 2.3 2.4 2.5
2.6 2.7 2.8 MEASURABLE FUNCTIONS INTEGRATION OF NONNEGATIVE FUNCTIONS
INTEGRATION OFCOMPLEX FUNCTIONS MODES OF CONVERGENCE PRODUCT MEASURES
THE N-DIMENSIONAL LEBESGUE INTEGRAL INTEGRATION IN POLAR COORDINATES
NOTES AND REFERENCES SIGNED MEASURES AND DIFFERENTIATION 3.1 3.2 3.3 3.4
3.5 3.6 SIGNED MEASURES THE LEBESGUE-RADON-NIKODYM THEOREM COMPLEX
MEASURES DIFFERENTIATION ON EUCLIDEAN SPACE FUNCTIONS OFBOUNDED
VARIATION NOTES AND REFERENCES POINT SET TOPOLOGY 4.1 4.2 4.3 4.4 4.5
4.6 4.7 4.8 4.9 TOPOLOGICAL SPACES CONTINUOUS MOPS NETS COMPACT SPACES
LOCALLY COMPACT HAUSDORFF SPACES TWO COMPACTNESS THEOREMS THE
STONE-WEIERSTRASS THEOREM EMBEDDINGS IN CUBES NOTES AND REFERENCES
ELEMENTS OF FUNCTIONAL ANALYSIS 5.1 5.2 5.3 5.4 5.5 5.6 NORMED VECTOR
SPACES LINEAR FUNCTIONALS THE BAIRE CATEGORY THEOREM AND ITS
CONSEQUENCES TOPOLOGICAL VECTOR SPACES HUBERT SPACES NOTES AND
REFERENCES 43 43 49 52 60 64 70 77 81 85 85 88 93 95 100 109 113 113 119
125 128 131 136 138 143 146 151 151 157 161 165 171 179 CONTENTS XIII 6
V SPACES 181 6.1 BASIC THEORY OF L P SPACES 181 6.2 THE DUAL OFU 188
6.3 SOME USEFUL INEQUALITIES 193 6.4 DISTRIBUTION FUNCTIONS AND WEAK V
197 6.5 INTERPOLATION OFU SPACES 200 6.6 NOTES AND REFERENCES 208 7
RADON MEASURES 211 7.1 POSITIVE LINEAR FUNCTIONALS ON C C {X) 211 7.2
REGULARITY AND APPROXIMATION THEOREMS 216 7.3 THE DUAL OFC 0 (X) 221 7.4
PRODUCTS OF RADON MEASURES 226 7.5 NOTES AND REFERENCES 231 8 ELEMENTS
OF FOURIER ANALYSIS 235 8.1 PRELIMINARIES 235 8.2 CONVOLUTIONS 239 8.3
THE FOURIER TRANSFORM 247 8.4 SUMMATION OFFOURIER INTEGRALS AND SERIES
257 8.5 POINTWISE CONVERGENCE OFFOURIER SERIES 263 8.6 FOURIER ANALYSIS
OF MEASURES 270 8.7 APPLICATIONS TO PARTIAL DIFFERENTIAL EQUATIONS 273
8.8 NOTES AND REFERENCES 278 9 ELEMENTS OF DISTRIBUTION THEORY 281 9.1
DISTRIBUTIONS 281 9.2 COMPACTLY SUPPORTED, TEMPERED, AND PERIODIC
DISTRIBUTIONS 291 9.3 SOBOLEV SPACES 301 9.4 NOTES AND REFERENCES 310 10
TOPICS IN PROBABILITY THEORY 313 10.1 BASIC CONCEPTS 313 10.2 THE LAW
OFLARGE NUMBERS 320 10.3 THE CENTRAL LIMIT THEOREM 325 10.4 CONSTRUCTION
OF SAMPLE SPACES 328 10.5 THE WIENER PROCESS 330 10.6 NOTES AND
REFERENCES 336 K XIV CONTENTS 11 MORE MEASURES AND INTEGRALS 339 11.1
TOPOLOGICAL GROUPS AND HAAR MEASURE 339 11.2 HAUSDORFF MEASURE 348 11.3
SELF-SIMILARITY AND HAUSDORFF DIMENSION 355 11.4 INTEGRATION ON
MANIFOLDS 361 11.5 NOTES AND REFERENCES 363 BIBLIOGRAPHY 365 INDEX OF
NOTATION 377 INDEX 379 |
| any_adam_object | 1 |
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| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Second edition |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-11-08T11:01:19Z |
| institution | BVB |
| isbn | 9780471317166 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008586418 |
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| physical | xiv, 386 Seiten Illustrationen |
| publishDate | 1999 |
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| series2 | Pure and applied mathematics |
| spelling | Folland, Gerald B. 1947- Verfasser (DE-588)137062486 aut Real analysis modern techniques and their applications Gerald B. Folland Second edition New York Wiley [1999] © 1999 xiv, 386 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics Reelle Analysis (DE-588)4627581-2 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Reelle Analysis (DE-588)4627581-2 s DE-604 Analysis (DE-588)4001865-9 s GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008586418&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Folland, Gerald B. 1947- Real analysis modern techniques and their applications Reelle Analysis (DE-588)4627581-2 gnd Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4627581-2 (DE-588)4001865-9 |
| title | Real analysis modern techniques and their applications |
| title_auth | Real analysis modern techniques and their applications |
| title_exact_search | Real analysis modern techniques and their applications |
| title_full | Real analysis modern techniques and their applications Gerald B. Folland |
| title_fullStr | Real analysis modern techniques and their applications Gerald B. Folland |
| title_full_unstemmed | Real analysis modern techniques and their applications Gerald B. Folland |
| title_short | Real analysis |
| title_sort | real analysis modern techniques and their applications |
| title_sub | modern techniques and their applications |
| topic | Reelle Analysis (DE-588)4627581-2 gnd Analysis (DE-588)4001865-9 gnd |
| topic_facet | Reelle Analysis Analysis |
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