{"product_id":"topics-on-analysis-in-metric-spaces","title":"Topics on Analysis in Metric Spaces","description":"\u003cp\u003eBased 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.\u003c\/p\u003e","brand":"Luigi Ambrosio","offers":[{"title":"Default Title","offer_id":43575267295293,"sku":"9780198529385","price":241.0,"currency_code":"AUD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0597\/7689\/2989\/files\/9780198529385.jpg?v=1788561664","url":"https:\/\/www.palmleaf.com.au\/products\/topics-on-analysis-in-metric-spaces","provider":"Palmleaf","version":"1.0","type":"link"}