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Metrics for sets of convex bodies

Published online by Cambridge University Press:  26 February 2010

G. C. Shephard  and
R. J. Webster
G. C. Shephard
Affiliation:
Department of Pure Mathematics, The University, Birmingham, 15
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Extract

In many investigations into the properties of convex bodies, authors have made use of distance functions ρ(K1K2) which give a measure of the “nearness” of two convex bodies K1 and K2. Sometimes they have introduced new functions to deal with particular problems. The purpose of this paper is to compare and contrast the properties of four of these functions, namely all those (so far as we are aware) which occur in the literature and have the property that they are metrics on the set of all convex bodies of some given dimension.

Type
Research Article
Information
Mathematika , Volume 12 , Issue 1 , June 1965 , pp. 73 - 88
Copyright
Copyright © University College London 1965

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