About: Brunn–Minkowski theorem

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In mathematics, the Brunn–Minkowski theorem (or Brunn–Minkowski inequality) is an inequality relating the volumes (or more generally Lebesgue measures) of compact subsets of Euclidean space. The original version of the Brunn–Minkowski theorem (Hermann Brunn 1887; Hermann Minkowski 1896) applied to convex sets; the generalization to compact nonconvex sets stated here is due to Lazar Lyusternik (1935).

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rdf:type	yago:WikicatTheoremsInConvexGeometry yago:WikicatTheoremsInMeasureTheory yago:Abstraction100002137 yago:Attribute100024264 yago:Communication100033020 yago:Difference104748836 yago:Inequality104752221 yago:Message106598915 yago:Proposition106750804 yago:Quality104723816 yago:WikicatGeometricInequalities yago:Statement106722453 yago:Theorem106752293
rdfs:label	Brunn-Minkowski-Ungleichung (de) Teorema de Brunn-Minkowski (es) Brunn–Minkowski theorem (en) Teorema di Brunn-Minkowski (it) Неравенство Брунна — Минковского (ru) Brunn–Minkowskis sats (sv)
rdfs:comment	Die Brunn-Minkowski-Ungleichung bzw. der Satz von Brunn und Minkowski, benannt nach den beiden Mathematikern Hermann Brunn und Hermann Minkowski, ist ein klassischer Lehrsatz auf dem mathematischen Teilgebiet der Konvexgeometrie. Die Ungleichung setzt das Lebesgue-Maß der Minkowski-Summe zweier kompakter Teilmengen des n-dimensionalen euklidischen Raums in Relation zum Lebesgue-Maß dieser beiden Teilmengen. Sie hat zahlreiche Anwendungen und zieht insbesondere die isoperimetrische Ungleichung nach sich. (de) In mathematics, the Brunn–Minkowski theorem (or Brunn–Minkowski inequality) is an inequality relating the volumes (or more generally Lebesgue measures) of compact subsets of Euclidean space. The original version of the Brunn–Minkowski theorem (Hermann Brunn 1887; Hermann Minkowski 1896) applied to convex sets; the generalization to compact nonconvex sets stated here is due to Lazar Lyusternik (1935). (en) En matemáticas, el teorema de Brunn-Minkowski (o desigualdad de Brunn-Minkowski) es una desigualdad que relaciona los volúmenes (o más generalmente medidas de Lebesgue) de subconjuntos compactos del espacio euclidiano. La versión original del teorema de Brunn-Minkowski (Hermann Brunn 1887; Hermann Minkowski 1896) se aplicó a conjuntos convexos; la generalización a conjuntos compactos no convexos que se indica aquí se debe a (1935). (es) In matematica, il teorema di Brunn-Minkowski (o disuguaglianza di Brunn-Minkowski) è una disuguaglianza che mette in relazione volumi (o, più in generale, misure di Lebesgue) di sottoinsiemi compatti di uno spazio euclideo. La versione originale del teorema di Brunn-Minkowski ( 1887; Hermann Minkowski 1896) si applicava a insiemi convessi; la generalizzazione a insiemi compatti non convessi a cui ci riferiamo qui è dovuta a (1935). (it) Inom matematiken är Brunn–Minkowski sats (eller Brunn–Minkowskis olikhet) en olikhet mellan volymerna (eller mer allmänt Lebesguemåtten) av kompakta delrum av ett Euklidiskt rum. Den ursprungliga formen av satsen ( 1887; Hermann Minkowski 1896) gällde konvexa mängder; generaliseringen till kompakta icke-konvexa mängder bevisades av (1935). (sv) Теорема Брунна — Минковского — классическая теорема выпуклой геометрии: (ru)
dcterms:subject	Theorems in convex geometry Theorems in measure theory Geometric inequalities Calculus of variations Sumsets Hermann Minkowski
Wikipage page ID	7500545 (xsd:integer)
Wikipage revision ID	1117660941 (xsd:integer)
Link from a Wikipage to another Wikipage	Prékopa–Leindler inequality Rolf Schneider Homothetic transformation Compact space Convex set Analytic set Mathematics Modulus and characteristic of convexity Theorems in convex geometry Theorems in measure theory Concave function Concentration of measure Milman's reverse Brunn–Minkowski inequality Geometric inequalities Calculus of variations Heinrich Guggenheimer Lebesgue measure Minkowski–Steiner formula Sumsets Euclidean space Isoperimetric inequality Hermann Brunn Hermann Minkowski Hermann Minkowski Lazar Lyusternik Translation (geometry) Mixed volume Inequality (mathematics) Inequality of arithmetic and geometric means Brunn–Minkowski theorem Young's inequality for products Scaling (geometry) Regularity theorem for Lebesgue measure Vitale's random Brunn–Minkowski inequality Subset Minkowski sum
Link from a Wikipage to an external page	http://sbubeck.com/Bubeck15.pdf http://www.math.lsa.umich.edu/~barvinok/total710.pdf https://projecteuclid.org/euclid.rae/1212412875 https://archive.org/details/theoryofconvexbo0000bonn https://www.ams.org/journals/bull/2002-39-03/S0273-0979-02-00941-2/ https://www.youtube.com/watch%3Fv=5YI6wKw2Jdo https://www.youtube.com/watch%3Fv=UHvT1MxFuvo https://cs.uwaterloo.ca/~lapchi/cs798/L19.pdf https://cs.uwaterloo.ca/~lapchi/cs798/L20.pdf
sameAs	Brunn–Minkowski theorem Brunn–Minkowski theorem Brunn–Minkowski theorem Brunn–Minkowski theorem Brunn–Minkowski theorem Brunn–Minkowski theorem Brunn–Minkowski theorem Brunn–Minkowski theorem Brunn–Minkowski theorem Brunn–Minkowski theorem
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has abstract	Die Brunn-Minkowski-Ungleichung bzw. der Satz von Brunn und Minkowski, benannt nach den beiden Mathematikern Hermann Brunn und Hermann Minkowski, ist ein klassischer Lehrsatz auf dem mathematischen Teilgebiet der Konvexgeometrie. Die Ungleichung setzt das Lebesgue-Maß der Minkowski-Summe zweier kompakter Teilmengen des n-dimensionalen euklidischen Raums in Relation zum Lebesgue-Maß dieser beiden Teilmengen. Sie hat zahlreiche Anwendungen und zieht insbesondere die isoperimetrische Ungleichung nach sich. (de) In mathematics, the Brunn–Minkowski theorem (or Brunn–Minkowski inequality) is an inequality relating the volumes (or more generally Lebesgue measures) of compact subsets of Euclidean space. The original version of the Brunn–Minkowski theorem (Hermann Brunn 1887; Hermann Minkowski 1896) applied to convex sets; the generalization to compact nonconvex sets stated here is due to Lazar Lyusternik (1935). (en) En matemáticas, el teorema de Brunn-Minkowski (o desigualdad de Brunn-Minkowski) es una desigualdad que relaciona los volúmenes (o más generalmente medidas de Lebesgue) de subconjuntos compactos del espacio euclidiano. La versión original del teorema de Brunn-Minkowski (Hermann Brunn 1887; Hermann Minkowski 1896) se aplicó a conjuntos convexos; la generalización a conjuntos compactos no convexos que se indica aquí se debe a (1935). (es) In matematica, il teorema di Brunn-Minkowski (o disuguaglianza di Brunn-Minkowski) è una disuguaglianza che mette in relazione volumi (o, più in generale, misure di Lebesgue) di sottoinsiemi compatti di uno spazio euclideo. La versione originale del teorema di Brunn-Minkowski ( 1887; Hermann Minkowski 1896) si applicava a insiemi convessi; la generalizzazione a insiemi compatti non convessi a cui ci riferiamo qui è dovuta a (1935). (it) Inom matematiken är Brunn–Minkowski sats (eller Brunn–Minkowskis olikhet) en olikhet mellan volymerna (eller mer allmänt Lebesguemåtten) av kompakta delrum av ett Euklidiskt rum. Den ursprungliga formen av satsen ( 1887; Hermann Minkowski 1896) gällde konvexa mängder; generaliseringen till kompakta icke-konvexa mängder bevisades av (1935). (sv)

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