These notes originated from a course given by the first author in 1998/99 in the Scuola Normale Superiore of Pisa. The aim of the course was the presentation of the main mathematical prerequisites needed for the so-called Analysis in Metric Spaces. The exposition, though not fully self contained, covers abstract measure theory, Hausdorff measures, Lipschitz functions, covering theorems, Sobolev spaces; all these topics are developed in a general metric setting. We also discuss in detail the geodesic problem and the Gromov-Hausdorff convergence. The last chapter contains a brief, but very general, description of the theory of integration with respect to nondecreasing set functions.
- ISBN13 9788876422652
- Publish Date 1 October 2000
- Publish Status Active
- Publish Country IT
- Publisher Birkhauser Verlag AG
- Imprint Scuola Normale Superiore
- Format Paperback
- Pages 133
- Language English