Topics on analysis in metric spaces:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Oxford Univ. Pr.
2004
|
| Edition: | 1. publ. |
| Series: | Oxford lecture series in mathematics and its applications
25 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | VIII, 133 S. |
| ISBN: | 0198529384 |
Staff View
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| 245 | 1 | 0 | |a Topics on analysis in metric spaces |c Luigi Ambrosio and Paolo Tilli |
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Record in the Search Index
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| adam_text | Titel: Topics on analysis in metric spaces
Autor: Ambrosio, Luigi
Jahr: 2004
Contents
1 Some preliminaries on measure theory 1
1.1 Outer measures 1
1.2 Signed and vector measures 9
1.3 Weak convergence of measures 14
Exercises 17
2 HausdorfF measures and covering theorems in
metric spaces 19
2.1 Hausdorff measures 19
Exercises 22
2.2 Covering theorems 23
2.3 Relationships between Hausdorff and Lebesgue
measures 28
2.4 Densities 30
Exercises 32
3 Lipschitz functions in metric spaces 35
3.1 Definition and general properties 35
Exercises 39
3.2 Lipschitz functions of several real variables 39
Exercise 43
3.3 The area formula 44
3.4 The one-dimensional area formula 45
Exercises 51
4 The geodesic problem and Gromov-HausdorfF
convergence 53
4.1 Metric derivative and geodesies in metric spaces 54
Exercises 58
4.2 Reparametrization 59
4.3 Existence of geodesies 61
Exercises 63
4.4 The intrinsic formulation 64
Exercises 79
viii Contents
4.5 Gromov-Hausdorff convergence of metric spaces 79
Exercises 86
5 Sobolev spaces in a metric framework 89
5.1 Definition of metric Sobolev spaces 89
5.2 Doubling measures and maximal operators 92
Exercises 98
5.3 Equivalence between classical and metric Sobolev
spaces 98
Exercise 100
5.4 Poincare and Sobolev inequalities 101
Exercises 110
6 A quick overview on the theory of integration 113
6.1 The Archimedean integral 114
6.2 Integration with respect to nondecreasing set
functions 114
6.3 Integral of extended real-valued functions 121
Bibliography 125
Index 131
|
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| author | Ambrosio, Luigi 1963- Tilli, Paolo |
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| author_variant | l a la p t pt |
| building | Verbundindex |
| bvnumber | BV019292009 |
| callnumber-first | Q - Science |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SD 1998 SK 280 |
| classification_tum | MAT 546f |
| ctrlnum | (OCoLC)249079183 (DE-599)BVBBV019292009 |
| dewey-full | 514.325 516.1 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology 516 - Geometry |
| dewey-raw | 514.325 516.1 |
| dewey-search | 514.325 516.1 |
| dewey-sort | 3514.325 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| institution | BVB |
| isbn | 0198529384 |
| language | English |
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| physical | VIII, 133 S. |
| publishDate | 2004 |
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| publisher | Oxford Univ. Pr. |
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| series | Oxford lecture series in mathematics and its applications |
| series2 | Oxford lecture series in mathematics and its applications |
| spelling | Ambrosio, Luigi 1963- Verfasser (DE-588)133791408 aut Topics on analysis in metric spaces Luigi Ambrosio and Paolo Tilli 1. publ. Oxford Oxford Univ. Pr. 2004 VIII, 133 S. txt rdacontent n rdamedia nc rdacarrier Oxford lecture series in mathematics and its applications 25 Hier auch später erschienene, unveränderte Nachdrucke Mathematical analysis Metric spaces Metrischer Raum (DE-588)4169745-5 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 1998-1999 Pisa gnd-content Metrischer Raum (DE-588)4169745-5 s b DE-604 Tilli, Paolo Verfasser aut Oxford lecture series in mathematics and its applications 25 (DE-604)BV009910017 25 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012043610&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ambrosio, Luigi 1963- Tilli, Paolo Topics on analysis in metric spaces Oxford lecture series in mathematics and its applications Mathematical analysis Metric spaces Metrischer Raum (DE-588)4169745-5 gnd |
| subject_GND | (DE-588)4169745-5 (DE-588)1071861417 |
| title | Topics on analysis in metric spaces |
| title_auth | Topics on analysis in metric spaces |
| title_exact_search | Topics on analysis in metric spaces |
| title_full | Topics on analysis in metric spaces Luigi Ambrosio and Paolo Tilli |
| title_fullStr | Topics on analysis in metric spaces Luigi Ambrosio and Paolo Tilli |
| title_full_unstemmed | Topics on analysis in metric spaces Luigi Ambrosio and Paolo Tilli |
| title_short | Topics on analysis in metric spaces |
| title_sort | topics on analysis in metric spaces |
| topic | Mathematical analysis Metric spaces Metrischer Raum (DE-588)4169745-5 gnd |
| topic_facet | Mathematical analysis Metric spaces Metrischer Raum Konferenzschrift 1998-1999 Pisa |
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