02533nam a22003855a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016707200170018408400290020110000330023024500980026326000820036130000340044333600260047733700260050333800360052934700240056549000510058950600660064052011510070665000320185765000350188965000330192465000240195765000660198185600320204785600680207967-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20080212sz fot ||| 0|eng d a978303719544470a10.4171/0442doi ach0018173 7aPBKG2bicssc 7aPBKQ2bicssc a28-xxa26-xxa49-xx2msc1 aDe Lellis, Camillo,eauthor.10aRectifiable Sets, Densities, and Tangent Measuresh[electronic resource] /cCamillo De Lellis3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2008 a1 online resource (133 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 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.07aFunctional analysis2bicssc07aCalculus of variations2bicssc07aMeasure and integration2msc07aReal functions2msc07aCalculus of variations and optimal control; optimization2msc40uhttps://doi.org/10.4171/044423cover imageuhttps://www.ems-ph.org/img/books/delellis_mini.jpg