02689nam 22004575a 450 991015193560332120091109150325.03-03719-544-410.4171/044(CKB)3710000000953819(CH-001817-3)67-091109(PPN)178155322(EXLCZ)99371000000095381920091109j20080212 fy 0engurnn|mmmmamaatxtrdacontentcrdamediacrrdacarrierRectifiable Sets, Densities, and Tangent Measures[electronic resource] /Camillo De LellisZuerich, Switzerland European Mathematical Society Publishing House20081 online resource (133 pages)Zurich Lectures in Advanced Mathematics (ZLAM)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.Functional analysisbicsscCalculus of variationsbicsscMeasure and integrationmscReal functionsmscCalculus of variations and optimal control; optimizationmscFunctional analysisCalculus of variationsMeasure and integrationReal functionsCalculus of variations and optimal control; optimization28-xx26-xx49-xxmscDe Lellis Camillo471661ch0018173BOOK9910151935603321Rectifiable sets, densities and tangent measures229597UNINA