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Birkhäuser - Birkhäuser Mathematics - Scuola Normale Superiore | Selected topics on Analysis in Metric Spaces

Selected topics on Analysis in Metric Spaces

Ambrosio, Luigi, Till, Paolo

133 p.

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  • About this book

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.

Content Level » Research

Keywords » analysis in metric spaces

Related subjects » Scuola Normale Superiore

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