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.
- ISBN10 0198529384
- ISBN13 9780198529385
- Publish Date 18 December 2003
- Publish Status Active
- Publish Country GB
- Imprint Oxford University Press
- Format Hardcover
- Pages 142
- Language English