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Rectifiable Sets, Densities, and Tan...

De Lellis, Camillo,

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Rectifiable Sets, Densities, and Tangent Measures

Record Type:	Electronic resources : Monograph/item
Title/Author:	Rectifiable Sets, Densities, and Tangent Measures/ Camillo De Lellis
Author:	De Lellis, Camillo,
Published:	Zuerich, Switzerland :European Mathematical Society Publishing House, : 2008,
Description:	1 online resource (133 pages)
Subject:	Measure and integration -
Online resource:	https://doi.org/10.4171/044
Online resource:	https://www.ems-ph.org/img/books/delellis_mini.jpg
ISBN:	9783037195444

Rectifiable Sets, Densities, and Tangent Measures
De Lellis, Camillo,

Rectifiable Sets, Densities, and Tangent Measures[electronic resource] /Camillo De Lellis - Zuerich, Switzerland :European Mathematical Society Publishing House,2008 - 1 online resource (133 pages) - Zurich Lectures in Advanced Mathematics (ZLAM).

Restricted to subscribers:https://www.ems-ph.org/ebooks.php

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.

ISBN: 9783037195444

Standard No.: 10.4171/044doiSubjects--Topical Terms:

3480901
Measure and integration

Rectifiable Sets, Densities, and Tangent Measures
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520 $a 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.
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