Topics on Analysis in Metric Spaces (Innbundet)

Serie: Oxford Lecture Series in Mathematics and Its Applications 25



Forfatter: og
Innbinding: Innbundet
Utgivelsesår: 2003
Antall sider: 142
Forlag: Oxford University Press
Språk: Engelsk
Serienummer: 25
ISBN/EAN: 9780198529385
Kategori: Matematikk
Omtale Topics on Analysis in Metric Spaces
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.

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