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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(EXLCZ)994100000011401198
100   $a20210806h2020      uy             0
101 0 $aeng
135   $aurcnu||||||||
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aLectures on Convex Geometry$b[electronic resource] /$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 $aGraduate Texts in Mathematics,$x0072-5285 ;$v286
311   $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,$x0072-5285 ;$v286
606   $aConvex geometry 
606   $aDiscrete geometry
606   $aPolytopes
606   $aMeasure theory
606   $aFunctional analysis
606   $aConvex and Discrete Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21014
606   $aPolytopes$3https://scigraph.springernature.com/ontologies/product-market-codes/M21040
606   $aMeasure and Integration$3https://scigraph.springernature.com/ontologies/product-market-codes/M12120
606   $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066
615  0$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
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   $a996418271503316
996   $aLectures on Convex Geometry$92547512
997   $aUNISA