×

Gewichtete Volumsmittelwerte von Simplices, welche zufällig in einem konvexen Körper des \(R^n\) gewählt werden. (German) Zbl 0383.52011


MSC:

52A40 Inequalities and extremum problems involving convexity in convex geometry
52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces)
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[1] Blaschke, W.: ?ber affine Geometrie XI: L?sung des Vierpunktproblems von Sylvester aus der Theorie der geometrischen Wahrscheinlichkeiten. Ber. Verh. s?chs. Akad. Leipzig69, 436-453 (1917).
[2] Blaschke, W.: Vorlesungen ?ber Differentialgeometrie II: Affine Differentialgeometrie. Berlin: J. Springer. 1923. · JFM 49.0499.01
[3] Bonnesen, T., undW. Fenchel: Theorie der konvexen K?rper. Ergebn. d. Math. Bd. 3. Berlin: J. Springer. 1936.
[4] Groemer, H.: On some mean values associated with a randomly selected simplex in a convex set. Pac. J. Math.45, 525-533 (1973). · Zbl 0258.52004
[5] Groemer, H.: On the mean value of the volume of a random polytope in a convex set. Arch. Math.25, 86-90 (1974). · Zbl 0287.52009 · doi:10.1007/BF01238645
[6] Hadwiger, H.: Konkave Eik?rperfunktionale und h?here Tr?gheitsmomente. Comm. Math. Helv.30, 285-296 (1956). · Zbl 0073.17305 · doi:10.1007/BF02564348
[7] Kingman, J. F. C.: Random secants of a convex body. J. Appl. Prob.6, 660-672 (1969). · Zbl 0186.51603 · doi:10.2307/3212110
[8] Klee, V.: What is the expected volume of a simplex, whose vertices are chosen at random from a given convex body? Am. Math. Monthly76, 286-288 (1969). · doi:10.2307/2316377
[9] Valentine, F. A.: Konvexe Mengen. Hochschultaschenb?cher Bd. 402/402a. Mannheim: Bibliograph. Institut. 1968.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.