Topics on Analysis in Metric Spaces (Oxford Lecture Series in Mathematics and Its Applications)

Topics on Analysis in Metric Spaces (Oxford Lecture Series in Mathematics and Its Applications) by Luigi Ambrosio epub pdf fb2

Title: Topics on Analysis in Metric Spaces (Oxford Lecture Series in Mathematics and Its Applications)
Author: Luigi Ambrosio
ISBN10: 0198529384
ISBN13: 978-0198529385
Publisher: Oxford University Press; 1 edition (February 26, 2004)
Language: English
Subcategory: Mathematics
Size PDF: 1612 kb
Size Fb2: 1452 kb
Rating: 4.6/5
Votes: 333
Pages: 144 pages
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Topics on Analysis in Metric Spaces (Oxford Lecture Series in Mathematics and Its Applications) by Luigi Ambrosio


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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.