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2 results

  • THE AVERAGE DISTANCE BETWEEN TWO POINTS

  • Part of
  • BERNHARD BURGSTALLER, FRIEDRICH PILLICHSHAMMER
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 80 / Issue 3 / December 2009
    Published online by Cambridge University Press:
    02 October 2009, pp. 353-359
    Print publication:
    December 2009
    • Article
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  • We provide bounds on the average distance between two points uniformly and independently chosen from a compact convex subset of the s-dimensional Euclidean space.

  • The average distance between two convex sets

  • H. Groemer
  • Journal:
    Journal of Applied Probability / Volume 17 / Issue 2 / June 1980
    Published online by Cambridge University Press:
    14 July 2016, pp. 415-422
    Print publication:
    June 1980

  • In recent publications of Hadwiger, Bokowski, and Wills it has been shown that it is possible to evaluate the average distance between a fixed and a randomly distributed convex set in terms of the mean projection measures of these sets. In the present note it is pointed out that these and more general results can be obtained from a theorem concerning the relationship between integrals over arbitrary measure spaces and corresponding Lebesgue–Stieltjes integrals.