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Epsilon entropy and the packing of balls in Euclidean space

Part of: Classical measure theory

Published online by Cambridge University Press:  26 February 2010

John Hawkes
John Hawkes
Affiliation:
Department of Mathematics, University College of Swansea, Singleton Park, Swansea. SA2 8PP.
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Summary

Let be a sequence of mutually disjoint open balls, with centres xj and corresponding radii aj, each contained in the closed unit ball in d-dimensional euclidean space, ℝd. Further we suppose, for simplicity, that the balls Bj are indexed so that aj≥aj+1. The set

obtained by removing, from the balls {Bj} is called the residual set. We say that the balls {Bj} constitute a packing of provided that λ(ℛ)=0, where λ denotes the d-dimensional Lebesgue measure. Thus it follows that henceforth denoted by c(d), whilst the packing restraint ensures that Larman [11] has noted that, under these circumstances, one also has .

MSC classification

Secondary: 28A80: Fractals
Type
Research Article
Information
Mathematika , Volume 43 , Issue 1 , June 1996 , pp. 23 - 31
Copyright
Copyright © University College London 1996

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