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Item Details
Title: TOPICS ON ANALYSIS IN METRIC SPACES
By: Luigi Ambrosio, Paolo Tilli
Format: Hardback

List price: £95.00
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ISBN 10: 0198529384
ISBN 13: 9780198529385
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Publisher: OXFORD UNIVERSITY PRESS
Pub. date: 18 December, 2003
Series: Oxford Lecture Series in Mathematics and Its Applications 25
Pages: 142
Description: Based on lecture notes from the 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.
Synopsis: Based on lecture notes from the 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. The book covers abstract measure theory, Hausdorff measures, Lipschitz functions, covering theorems, lower semicontinuity of the one-dimensional Hausdorff measure, Sobolev spaces of maps between metric spaces, and Gromov-Hausdorff theory, all developed in a general metric setting. The existence of geodesics (and more generally of minimal Steiner connections) is discussed in 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 Cavalieri's formula as the definition of the integral.
Illustrations: numerous line drawings
Publication: UK
Imprint: Oxford University Press
Returns: Returnable
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