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Bibliographic Details
Main Authors:	Ambrosio, Luigi 1963- (Author), Tilli, Paolo (Author)
Format:	Book
Language:	English
Published:	Oxford Oxford Univ. Pr. 2004
Edition:	1. publ.
Series:	Oxford lecture series in mathematics and its applications 25
Subjects:	Mathematical analysis Metric spaces Metrischer Raum Konferenzschrift > 1998-1999 > Pisa
Links:	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
Item Description:	Hier auch später erschienene, unveränderte Nachdrucke
Physical Description:	VIII, 133 S.
ISBN:	0198529384

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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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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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work_keys_str_mv	AT ambrosioluigi topicsonanalysisinmetricspaces AT tillipaolo topicsonanalysisinmetricspaces

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Call Number:	0102 MAT 546f 2001 A 5437 Floor plan
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