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An average distance result in Euclidean n-space

Published online by Cambridge University Press:  17 April 2009

John Strantzen
John Strantzen
Affiliation:
Department of Pure Mathematics, La Trobe University, Bundoora, Victoria 3083, Australia.
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The following result has been established by Stadje and Gross:

THEOREM. If 〈X, d〉 is a compact connected metric space, then there is a unique positive real number a(〈X, d〉) with the property that for each natural number n, and for all {x1, x2, …, xn} ⊂ X, there exists y ∈ X for which

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 26 , Issue 3 , December 1982 , pp. 321 - 330
Copyright
Copyright © Australian Mathematical Society 1982

References

[1]Blumenthal, L.M. and Wahlin, G.E., “On the spherical surface of smallest radius enclosing a bounded subset of n-dimensional Euclidean space”, Bull. Amer. Math. Soc. 47 (1941), 771–777.CrossRefGoogle Scholar
[2]Gross, O., “The rendezvous value of a metric space”, Advances in game theory, 49–53 (Annals of Mathematics Studies, 52. Princeton University Press, Princeton, New Jersey, 1964).Google Scholar
[3]Jung, Heinrich, “Ueber die kleinste Kugel, die eine raumliche Figur einschliesst”, J. reine Angew. Math. 123 (1901), 241–257.Google Scholar
[4]Morris, Sidney A. and Nickolas, Peter, “On the average distance property of compact connected metric spaces”, Arch. Math. (to appear).Google Scholar
[5]Stadje, Wolfgang, “A property of compact connected spaces”, Arch. Math. (Basel) 36 (1981), 275–280.CrossRefGoogle Scholar
[6]Szekeres, E. and Szekeres, G., “The average distance theorem for compact convex regions”, Bull. Austral. Math. Soc. (to appear).Google Scholar
[7]Wilson, D.J., “A game with squared distance as payoff”, Bull. Austral. Math. Soc. (to appear).Google Scholar
[8]Yost, David, “Average distances in compact connected spaces”, Bull. Austral. Math. Soc. 26 (1982), 331–342.CrossRefGoogle Scholar