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The average distance between two convex sets

Published online by Cambridge University Press:  14 July 2016

H. Groemer
H. Groemer*
Affiliation:
The University of Arizona
*
∗Postal address: Department of Mathematics, The University of Arizona, Tucson, AZ 85721, U.S.A.
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Abstract

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.

Keywords

AVERAGE DISTANCEINTEGRAL GEOMETRIC MEAN VALUESKINEMATIC PRINCIPAL FORMULAMIXED VOLUMES
Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 2 , June 1980 , pp. 415 - 422
Copyright
Copyright © Applied Probability Trust 1980 

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Footnotes

Research supported by National Science Foundation Grant MCS 76–06111.

References

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