On the mean value of the volume of a random polytope in a convex set
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Publication:1846269
DOI10.1007/BF01238645zbMath0287.52009MaRDI QIDQ1846269
Publication date: 1974
Published in: Archiv der Mathematik (Search for Journal in Brave)
Geometric probability and stochastic geometry (60D05) Inequalities and extremum problems involving convexity in convex geometry (52A40) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Polytopes and polyhedra (52Bxx)
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Cites Work
- Unnamed Item
- Unnamed Item
- Konkave Eikörperfunktionale und höhere Trägheitsmomente
- Über das Löwnersche Ellipsoid und sein Analogon unter den einem Eikörper einbeschriebenen Ellipsoiden
- Über kennzeichnende Eigenschaften von Ellipsoiden und euklidischen Räumen. III
- On some mean values associated with a randomly selected simplex in a convex set
- Über kennzeichnende Eigenschaften von euklidischen Räumen und Ellipsoiden. II.
- Random secants of a convex body
- A Compactness Theorem For Affine Equivalence-Classes of Convex Regions