02533nam a22003855a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016707200170018408400290020110000330023024500980026326000820036130000340044333600260047733700260050333800360052934700240056549000510058950600660064052011510070665000320185765000350188965000330192465000240195765000660198185600320204785600680207967-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20080212sz fot ||| 0|eng d a978303719544470a10.4171/0442doi ach0018173 7aPBKG2bicssc 7aPBKQ2bicssc a28-xxa26-xxa49-xx2msc1 aDe Lellis, Camillo,eauthor.10aRectifiable Sets, Densities, and Tangent Measuresh[electronic resource] /cCamillo De Lellis3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2008 a1 online resource (133 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aZurich Lectures in Advanced Mathematics (ZLAM)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe 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.07aFunctional analysis2bicssc07aCalculus of variations2bicssc07aMeasure and integration2msc07aReal functions2msc07aCalculus of variations and optimal control; optimization2msc40uhttps://doi.org/10.4171/044423cover imageuhttps://www.ems-ph.org/img/books/delellis_mini.jpg