ENGLISH

Topics on Analysis in Metric Spaces

By Luigi Ambrosio , Paolo Tilli

Book information

Publisher
Oxford University Press, USA
Year
2004
ISBN
0198529384, 9780198529385
LCC
QA611.28 .A43 2004
Open Library ID
OL22572337M
Language
english
Format
DJVU
Filesize
5 MB (5625945 bytes)
Series
Oxford Lecture Series in Mathematics and Its Applications
Pages
144\144
Time added
2011-01-06 10:13:16

Description

This book presents the main mathematical prerequisites for analysis in metric spaces. It covers abstract measure theory, Hausdorff measures, Lipschitz functions, covering theorums, lower semicontinuity of the one-dimensional Hausdorff measure, Sobolev spaces of maps between metric spaces, and Gromov-Hausdorff theory, all developed ina general metric setting. The existence of geodesics (and more generally of minimal Steiner connections) is discussed on general metric spaces and as an application of the Gromov-Hausdorff theory, even in some cases when the ambient space is not locally compact. A brief and very general description of the theory of integration with respect to non-decreasing set functions is presented following the Di Giorgi method of using the 'cavalieri' formula as the definition of the integral. Based on lecture notes from Scuola Normale, this book presents the main mathematical prerequisites for analysis in metric spaces. Supplemented with exercises of varying difficulty it is ideal for a graduate-level short course for applied mathematicians and engineers.

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