Rectifiable Sets, Densities and Tangent Measures (Zurich Lectures in Advanced Mathematics) free ebook download.

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Rectifiable Sets, Densities and Tangent Measures (Zurich Lectures in Advanced Mathematics) free ebook download

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Date:	2021	Format:	pdf	Language:	English	ISBN/ASIN:	3037190442
Pages:	134	OCR:		Quality:		ISBN13:
Uploader:	risotor	Upload Date:	6/30/2022 12:31:13 PM

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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 Zurich. 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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Tags: Advanced Densities Lectures Mathematics Measures Rectifiable Sets Tangent Zurich

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