LEADER 03441nam 22007215 450 001 9910483883403321 005 20251113194149.0 010 $a3-030-50180-9 024 7 $a10.1007/978-3-030-50180-8 035 $a(OCoLC)1192490338 035 $a(CKB)4100000011401198 035 $a(MiAaPQ)EBC6320837 035 $a(DE-He213)978-3-030-50180-8 035 $a(PPN)250214938 035 $a(MiAaPQ)EBC6320734 035 $a(MiAaPQ)EBC31870681 035 $a(Au-PeEL)EBL31870681 035 $a(EXLCZ)994100000011401198 100 $a20200827d2020 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aLectures on Convex Geometry /$fby Daniel Hug, Wolfgang Weil 205 $a1st ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020. 215 $a1 online resource (300 pages) 225 1 $aGraduate Texts in Mathematics,$x2197-5612 ;$v286 311 08$a3-030-50179-5 320 $aIncludes bibliographical references and index. 327 $aPreface -- Preliminaries and Notation -- 1. Convex Sets -- 2. Convex Functions -- 3. Brunn-Minkowski Theory -- 4. From Area Measures to Valuations -- 5. Integral Geometric Formulas.-6. Solutions of Selected Exercises -- References -- Index. 330 $aThis book provides a self-contained introduction to convex geometry in Euclidean space. After covering the basic concepts and results, it develops Brunn?Minkowski theory, with an exposition of mixed volumes, the Brunn?Minkowski inequality, and some of its consequences, including the isoperimetric inequality. Further central topics are then treated, such as surface area measures, projection functions, zonoids, and geometric valuations. Finally, an introduction to integral-geometric formulas in Euclidean space is provided. The numerous exercises and the supplementary material at the end of each section form an essential part of the book. Convexity is an elementary and natural concept. It plays a key role in many mathematical fields, including functional analysis, optimization, probability theory, and stochastic geometry. Paving the way to the more advanced and specialized literature, the material will be accessible to students in the third year and can be covered in one semester. 410 0$aGraduate Texts in Mathematics,$x2197-5612 ;$v286 606 $aConvex geometry 606 $aDiscrete geometry 606 $aPolytopes 606 $aMeasure theory 606 $aFunctional analysis 606 $aConvex and Discrete Geometry 606 $aPolytopes 606 $aMeasure and Integration 606 $aFunctional Analysis 615 0$aConvex geometry. 615 0$aDiscrete geometry. 615 0$aPolytopes. 615 0$aMeasure theory. 615 0$aFunctional analysis. 615 14$aConvex and Discrete Geometry. 615 24$aPolytopes. 615 24$aMeasure and Integration. 615 24$aFunctional Analysis. 676 $a516.08 676 $a516.08 700 $aHug$b Daniel$4aut$4http://id.loc.gov/vocabulary/relators/aut$01065686 702 $aWeil$b Wolfgang$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910483883403321 996 $aLectures on Convex Geometry$92547512 997 $aUNINA