LEADER 02689nam 22004575a 450 001 9910151935603321 005 20091109150325.0 010 $a3-03719-544-4 024 70$a10.4171/044 035 $a(CKB)3710000000953819 035 $a(CH-001817-3)67-091109 035 $a(PPN)178155322 035 $a(EXLCZ)993710000000953819 100 $a20091109j20080212 fy 0 101 0 $aeng 135 $aurnn|mmmmamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aRectifiable Sets, Densities, and Tangent Measures$b[electronic resource] /$fCamillo De Lellis 210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2008 215 $a1 online resource (133 pages) 225 0 $aZurich Lectures in Advanced Mathematics (ZLAM) 330 $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 Zu?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. 606 $aFunctional analysis$2bicssc 606 $aCalculus of variations$2bicssc 606 $aMeasure and integration$2msc 606 $aReal functions$2msc 606 $aCalculus of variations and optimal control; optimization$2msc 615 07$aFunctional analysis 615 07$aCalculus of variations 615 07$aMeasure and integration 615 07$aReal functions 615 07$aCalculus of variations and optimal control; optimization 686 $a28-xx$a26-xx$a49-xx$2msc 700 $aDe Lellis$b Camillo$0471661 801 0$bch0018173 906 $aBOOK 912 $a9910151935603321 996 $aRectifiable sets, densities and tangent measures$9229597 997 $aUNINA