Modern real analysis:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
PWS Publ. Co.
1995
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 360 S. |
| ISBN: | 0534944043 |
Internformat
MARC
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Datensatz im Suchindex
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| adam_text | MODERN REAL ANALYSIS RONALD E GARIEPY UNIVERSITY OF KENTUCKY WILLIAM P.
ZIEMER INDIANA UNIVERSITY PWS PUBLISHING COMPANY L(T)P AN INTERNATIONAL
THOMSON PUBLISHING COMPANY BOSTON * ALBANY * BONN * CINCINNATI * DETROIT
* LONDON * MADRID * MELBOURNE * MEXICO CITY * NEW YORK * PARIS * SAN
FRANCISCO * SINGAPORE * TOKYO * TORONTO * WASHINGTON CONTENTS PREFACE V
CHAPTER 1 PRELIMINARIES 1 1.1 SETS 1 1.2 FUNCTIONS 3 1.3 SET THEORY 6
EXERCISES 8 CHAPTER 2 REAL, CARDINAL, AND ORDINAL NUMBERS 10 10 20 27 32
2.1 2.2 *2.3 THE REAL NUMBERS CARDINAL NUMBERS ORDINAL NUMBERS EXERCISES
CHAPTER 3.1 3.2 3.3 3.4 3.5 3.6 3.7 *3.8 3 ELEMENTS OF TOPOLOC
TOPOLOGICAL SPACES BASES FOR A TOPOLOGY METRIC SPACES MEAGER SETS IN
TOPOLOGY COMPACTNESS IN METRIC SPACES COMPACTNESS OF PRODUCT SPACES THE
SPACE OF CONTINUOUS FUNCTIONS LOWER SEMICONTINUOUS FUNCTIONS EXERCISES
CHAPTER 4.1 4.2 4.3 4.4 4.5 4.6 4 MEASURE THEORY OUTER MEASURE
CARATHEODORY OUTER MEASURE LEBESGUE MEASURE THE CANTOR SET EXISTENCE OF
NONMEASURABLE SETS LEBESGUE-STIELTJES MEASURE INDICATES OPTIONAL
SECTIONS 34 38 40 44 46 49 51 58 62 67 75 81 87 88 90 34 67 IN *4.7
HAUSDORFF MEASURE 94 4.8 MEASURES ON ABSTRACT SPACES 99 4.9 OUTER
MEASURES GENERATED BY MEASURES 102 EXERCISES 107 CHAPTER 5 MEASURABLE
FUNCTIONS 111 5.1 ELEMENTARY PROPERTIES OF MEASURABLE FUNCTIONS 111 5.2
LIMITS OF MEASURABLE FUNCTIONS 121 5.3 THE APPROXIMABILITY OF MEASURABLE
FUNCTIONS 127 EXERCISES 131 CHAPTER 6 INTEGRATION 133 6.1 DEFINITIONS
AND ELEMENTARY PROPERTIES 133 6.2 LIMIT THEOREMS 138 6.3 RIEMANN AND
LEBESGUE INTEGRATION - A COMPARISON 141 6.4 LP SPACES 144 6.5 SIGNED
MEASURES 151 6.6 THE RADON-NIKODYM THEOREM 156 6.7 THE DUAL OF L^ 162
6.8 PRODUCT MEASURES AND FUBINI S THEOREM 168 6.9 LEBESGUE MEASURE AS A
PRODUCT MEASURE 176 6.10 CONVOLUTION 177 6.11 DISTRIBUTION FUNCTIONS 180
EXERCISES 183 CHAPTER 7 DIFFERENTIATION 190 7.1 COVERING THEOREMS 190
7.2 LEBESGUE POINTS 195 7.3 THE RADON-NIKODYM DERIVATIVE - ANOTHER VIEW
199 7.4 FUNCTIONS OF BOUNDED VARIATION 203 7.5 THE FUNDAMENTAL THEOREM
OF CALCULUS 208 *7.6 VARIATION OF CONTINUOUS FUNCTIONS 213 *7.7 CURVE
LENGTH ..... 217 *7.8 THE CRITICAL SET OF A FUNCTION 224 *7.9
APPROXIMATE CONTINUITY 230 EXERCISES ]] 235 CHAPTER 8 ELEMENTS OF
FUNCTIONAL ANALYSIS 241 8.1 NORMED LINEAR SPACES 241 8.2 HAHN-BANACH
THEOREM 249 8.3 CONTINUOUS LINEAR MAPPINGS 253 IV 8.4 DUAL SPACES 257
8.5 HILBERT SPACES 266 *8.6 WEAK AND STRONG CONVERGENCE IN L P 277
EXERCISES 282 CHAPTER 9 MEASURES AND LINEAR FUNCTIONALS 285 9.1 THE
DANIELL INTEGRAL . 285 9.2 THE RIESZ REPRESENTATION THEOREM 294
EXERCISES 302 CHAPTER 10 DISTRIBUTIONS 304 10.1 THE SPACE S 304 10.2
BASIC PROPERTIES OF DISTRIBUTIONS 309 10.3 DIFFERENTIATION OF
DISTRIBUTIONS 312 *10.4 ESSENTIAL VARIATION 317 EXERCISES 321 CHAPTER 11
FUNCTIONS OF SEVERAL VARIABLES 322 11.1 DIFFERENTIABILITY 322 11.2
CHANGE OF VARIABLE 326 11.3 SOBOLEV FUNCTIONS 336 11.4 APPROXIMATING
SOBOLEV FUNCTIONS 343 11.5 SOBOLEV IMBEDDING THEOREM 346 11.6
APPLICATIONS 349 11.7 REGULARITY OF WEAKLY HARMONIC FUNCTIONS 352
EXERCISES 355 REFERENCES 357 INDEX 358 NIEDERSACHST STAATS.U.UNIV.-
BIBLIOTHEK GDTTINGEN
|
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.8 |
| dewey-search | 515/.8 |
| dewey-sort | 3515 18 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV010766644 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:58:30Z |
| institution | BVB |
| isbn | 0534944043 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007189508 |
| oclc_num | 31515285 |
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| physical | VIII, 360 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | PWS Publ. Co. |
| record_format | marc |
| spelling | Gariepy, Ronald F. Verfasser aut Modern real analysis Ronald F. Gariepy ; William P. Ziemer Boston [u.a.] PWS Publ. Co. 1995 VIII, 360 S. txt rdacontent n rdamedia nc rdacarrier Functions of real variables Mathematical analysis Analysis (DE-588)4001865-9 gnd rswk-swf Analysis (DE-588)4001865-9 s DE-604 Ziemer, William P. Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007189508&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gariepy, Ronald F. Ziemer, William P. Modern real analysis Functions of real variables Mathematical analysis Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4001865-9 |
| title | Modern real analysis |
| title_auth | Modern real analysis |
| title_exact_search | Modern real analysis |
| title_full | Modern real analysis Ronald F. Gariepy ; William P. Ziemer |
| title_fullStr | Modern real analysis Ronald F. Gariepy ; William P. Ziemer |
| title_full_unstemmed | Modern real analysis Ronald F. Gariepy ; William P. Ziemer |
| title_short | Modern real analysis |
| title_sort | modern real analysis |
| topic | Functions of real variables Mathematical analysis Analysis (DE-588)4001865-9 gnd |
| topic_facet | Functions of real variables Mathematical analysis Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007189508&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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