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Rectifiable Sets, Densities and Tangent Measures

Camillo De Lellis University of Zürich, Zurich, Switzerland
A publication of European Mathematical Society
Available Formats:
Softcover ISBN: 978-3-03719-044-9
Product Code: EMSZLEC/7
List Price: $34.00 AMS Member Price:$27.20
This item is temporarily out of stock. Order now and your item will ship as soon as stock becomes available.
Expected availability date: May 28, 2023
Please note AMS points can not be used for this product
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Rectifiable Sets, Densities and Tangent Measures
Camillo De Lellis University of Zürich, Zurich, Switzerland
A publication of European Mathematical Society
Available Formats:
 Softcover ISBN: 978-3-03719-044-9 Product Code: EMSZLEC/7
 List Price: $34.00 AMS Member Price:$27.20
This item is temporarily out of stock. Order now and your item will ship as soon as stock becomes available.
Expected availability date: May 28, 2023
Please note AMS points can not be used for this product
• Book Details

EMS Zurich Lectures in Advanced Mathematics
Volume: 72008; 134 pp
MSC: Primary 28; 26; 49;

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 Zürich. 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.

Graduate students and research mathematicians interested in analysis.

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Volume: 72008; 134 pp
MSC: Primary 28; 26; 49;

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 Zürich. 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.