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The measure of the s-skeleton of a convex body

Published online by Cambridge University Press:  26 February 2010

G. R. Burton
G. R. Burton
Affiliation:
University College London.
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When K is a convex body in d-dimensional euclidean space E and 0 ≤ s ≤ d, the s-skeleton of K, denoted skel(s)K, consists of those points of K which are not centres of (s + l)-dimensional balls contained in K. The s-skeleton is thus the union of the extreme faces of K having dimension at most s. The s-skeleton is a -set [see 6] and it is therefore measurable with respect to the s-dimensional Hausdorff measure ℋ(s) [see 7]; here we normalize ℋ(s) so that it assigns unit measure to the s-dimensional unit cube.

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Type
Research Article
Information
Mathematika , Volume 26 , Issue 2 , December 1979 , pp. 290 - 301
Copyright
Copyright © University College London 1979

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