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On the mean value of the volume of a random polytope in a convex set

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References

  1. W. Blaschke, Über affine Geometrie XI: Lösung des „Vierpunktproblems“ von Sylvester aus der Theorie der geometrischen Wahrscheinlichkeiten. Ber. Verh. sächs. Akad. Leipzig69, 436–453 (1917).

    Google Scholar 

  2. W.Blaschke, Vorlesungen über Differentialgeometrie II: Affine Differentialgeometrie. Berlin 1923.

  3. T.Bonnesen und W.Fenchel, Theorie der konvexen Körper. Berlin 1934.

  4. L. Danzer, D. Laugwitz undH. Lenz, Über das Löwnersche Ellipsoid und sein Analogon unter den einem Eikörper einbeschriebenen Ellipsoiden. Arch. Math.8, 214–219 (1957).

    Google Scholar 

  5. H. Groemer, On some mean values associated with a randomly selected simplex in a convex set. Pacific J. Math.45, 525–533 (1973).

    Google Scholar 

  6. P.Gruber, Über kennzeichnende Eigenschaften von euklidischen Räumen und Ellipsoiden II. J. reine angew. Math, (in print).

  7. P.Gruber, Über kennzeichnende Eigenschaften von Ellipsoiden und euklidischen Räumen III. Monatsh. Math, (in print).

  8. H. Hadwiger, Konkave Eikörperfunktionale und höhere Trägheitsmomente. Comment. Math. Hélv.30, 285–296 (1956).

    Google Scholar 

  9. J. F. C. Kingman, Random secants of a convex body. J. Appl. Probability6, 660–672 (1969).

    Google Scholar 

  10. V. Klee, What is the expected volume of a simplex whose vertices are chosen at random from a given convex body? Amer. Math. Monthly76, 286–288 (1969).

    Google Scholar 

  11. A. M. Macbeath, An extremal property of the hypersphere. Proc. Cambridge Phil. Soc.47, 245–247 (1951).

    Google Scholar 

  12. A. M. Macbeath, A compactness theorem for affine equivalence classes of convex regions. Canad. J. Math.3, 54–61 (1951).

    Google Scholar 

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Supported by National Science Foundation Research Grant GP-34002.

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Groemer, H. On the mean value of the volume of a random polytope in a convex set. Arch. Math 25, 86–90 (1974). https://doi.org/10.1007/BF01238645

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