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Rectifiable Sets, Densities, and Tangent Measures
Zurich Lectures in Advanced Mathematics

Camillo De Lellis (University of Zurich)

Rectifiable Sets, Densities, and Tangent Measures

ISBN print 978-3-03719-044-9, ISBN online 978-3-03719-544-4
DOI 10.4171/044
February 2008, 133 pages, softcover, 17.0 x 24.0 cm.
26.00 Euro

The characterization of rectifiable sets through the existence of densities is a pearl of geometric measure theory. The difficult proof, due to Preiss, relies on many beautiful and deep ideas and novel techniques. Some of them have already proven useful in other contexts, whereas others have not yet been exploited. These notes give a simple and short presentation of the former, and provide some perspective of the latter.

This text emerged from a course on rectifiability given at the University of Z├╝rich. It is addressed both to researchers and students, the only prerequisite is a solid knowledge in standard measure theory. The first four chapters give an introduction to rectifiable sets and measures in euclidean spaces, covering classical topics such as the area formula, the theorem of Marstrand and the most elementary rectifiability criterions. The fifth chapter is dedicated to a subtle rectifiability criterion due to Marstrand and generalized by Mattila, and the last three focus on Preiss' result. The aim is to provide a self-contained reference for anyone interested in an overview of this fascinating topic.

Further Information

Review in Zentralblatt MATH 05236795

Review in MR 2388959 (2009j:28001)