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Topics on Analysis in Metric Spaces (Oxford Lecture Series in Mathematics and Its Applications),Used
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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 onedimensional Hausdorff measure, Sobolev spaces of maps between metric spaces, and GromovHausdorff 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 GromovHausdorff 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 nondecreasing 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 graduatelevel short course for applied mathematicians and engineers.
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