Measure theory and fine properties of functions:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
CRC Press
1992
|
| Schriftenreihe: | Studies in advanced mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 268 S. graph. Darst. |
| ISBN: | 0849371570 9780849371578 |
Internformat
MARC
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| 020 | |a 9780849371578 |9 978-0-8493-7157-8 | ||
| 035 | |a (OCoLC)243773322 | ||
| 035 | |a (DE-599)BVBBV008731543 | ||
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| 100 | 1 | |a Evans, Lawrence C. |d 1949- |e Verfasser |0 (DE-588)135567777 |4 aut | |
| 245 | 1 | 0 | |a Measure theory and fine properties of functions |c Lawrence C. Evans and Ronald F. Gariepy |
| 264 | 1 | |a Boca Raton [u.a.] |b CRC Press |c 1992 | |
| 300 | |a VIII, 268 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Studies in advanced mathematics | |
| 650 | 4 | |a Analyse fonctionnelle | |
| 650 | 7 | |a Analyse fonctionnelle |2 ram | |
| 650 | 4 | |a Mesure, Théorie de la | |
| 650 | 7 | |a Mesure, théorie de la |2 ram | |
| 650 | 4 | |a Functional analysis | |
| 650 | 4 | |a Measure theory | |
| 650 | 0 | 7 | |a Funktionalanalysis |0 (DE-588)4018916-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Maßtheorie |0 (DE-588)4074626-4 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Funktionalanalysis |0 (DE-588)4018916-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Gariepy, Ronald F. |e Verfasser |4 aut | |
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Datensatz im Suchindex
| _version_ | 1805082763492065280 |
|---|---|
| adam_text |
Contents
^
Preface vii
1 General Measure Theory 1
1.1 Measures and measurable functions 1
1.2 Lusin's and Egoroff's Theorems 13
1.3 Integrals and limit theorems 17
1.4 Product measures, Fubini's Theorem, Lebesgue measure 22
1.5 Covering theorems 26
1.6 Differentiation of Radon measures 37
1.7 Lebesgue points; Approximate continuity 43
1.8 Riesz Representation Theorem 49
1.9 Weak convergence and compactness for Radon measures 54
2, Hausdorff Measure 60
2.1 Definitions and elementary properties; Hausdorff
dimension 60
2.2 Isodiametric Inequality; 7in = Cn 65
2.3 Densities 71
2.4 Hausdorff measure and elementary properties of functions 75
J Area and Coarea Formulas 79
3.1 Lipschitz functions, Rademacher's Theorem 79
3.2 Linear maps and Jacobians 86
3.3 The Area Formula 92
3.4 The Coarea Formula 104
v
vi Contents
4 Sobolev Functions 120
4.1 Definitions and elementary properties 120
4.2 Approximation 122
4.3 Traces 133
4.4 Extensions 135
4.5 Sobolev inequalities 138
4.6 Compactness 144
4.7 Capacity 146
4.8 Quasicontinuity; Precise representatives of Sobolev
functions 158
4.9 Differentiability on lines 162
5 BV Functions and Sets of Finite Perimeter 166
5.1 Definitions; Structure Theorem 166
5.2 Approximation and compactness 172
5.3 Traces 176
5.4 Extensions 183
5.5 Coarea Formula for BV functions 185
5.6 Isoperimetric Inequalities 189
5.7 The reduced boundary 194
5.8 The measure theoretic boundary; Gauss Green Theorem 208
5.9 Pointwise properties of BV functions 209
5.10 Essential variation on lines 216
5.11 A criterion for finite perimeter 221 :
6 Differentiability and Approximation by C1 Functions 227
6.1 Lp differentiability; Approximate differentiability 227
6.2 Differentiability a.e. for Whp (p n) 234
6.3 Convex functions 236
6.4 Second derivatives a.e. for convex functions 241
6.5 Whitney's Extension Theorem 245
6.6 Approximation by C1 functions 251
Bibliography 257
Notation 261
Index 267 |
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| ctrlnum | (OCoLC)243773322 (DE-599)BVBBV008731543 |
| 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 |
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| id | DE-604.BV008731543 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T07:37:50Z |
| institution | BVB |
| isbn | 0849371570 9780849371578 |
| language | English |
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| physical | VIII, 268 S. graph. Darst. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | CRC Press |
| record_format | marc |
| series2 | Studies in advanced mathematics |
| spelling | Evans, Lawrence C. 1949- Verfasser (DE-588)135567777 aut Measure theory and fine properties of functions Lawrence C. Evans and Ronald F. Gariepy Boca Raton [u.a.] CRC Press 1992 VIII, 268 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Studies in advanced mathematics Analyse fonctionnelle Analyse fonctionnelle ram Mesure, Théorie de la Mesure, théorie de la ram Functional analysis Measure theory Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Maßtheorie (DE-588)4074626-4 gnd rswk-swf Maßtheorie (DE-588)4074626-4 s Funktionalanalysis (DE-588)4018916-8 s DE-604 Gariepy, Ronald F. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005761523&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Evans, Lawrence C. 1949- Gariepy, Ronald F. Measure theory and fine properties of functions Analyse fonctionnelle Analyse fonctionnelle ram Mesure, Théorie de la Mesure, théorie de la ram Functional analysis Measure theory Funktionalanalysis (DE-588)4018916-8 gnd Maßtheorie (DE-588)4074626-4 gnd |
| subject_GND | (DE-588)4018916-8 (DE-588)4074626-4 |
| title | Measure theory and fine properties of functions |
| title_auth | Measure theory and fine properties of functions |
| title_exact_search | Measure theory and fine properties of functions |
| title_full | Measure theory and fine properties of functions Lawrence C. Evans and Ronald F. Gariepy |
| title_fullStr | Measure theory and fine properties of functions Lawrence C. Evans and Ronald F. Gariepy |
| title_full_unstemmed | Measure theory and fine properties of functions Lawrence C. Evans and Ronald F. Gariepy |
| title_short | Measure theory and fine properties of functions |
| title_sort | measure theory and fine properties of functions |
| topic | Analyse fonctionnelle Analyse fonctionnelle ram Mesure, Théorie de la Mesure, théorie de la ram Functional analysis Measure theory Funktionalanalysis (DE-588)4018916-8 gnd Maßtheorie (DE-588)4074626-4 gnd |
| topic_facet | Analyse fonctionnelle Mesure, Théorie de la Mesure, théorie de la Functional analysis Measure theory Funktionalanalysis Maßtheorie |
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