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Dimension prints

Part of: Classical measure theory

Published online by Cambridge University Press:  26 February 2010

C. A. Rogers
C. A. Rogers
Affiliation:
Department of Statistical Science, University College London, Gower Street, London, WCIE 6BT
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Extract

The Hausdorff dimension has been used for many years for assessing the sizes of sets in Euclidean and other metric spaces, see, for example, [1,2,5,6,8,10]. However, different sets with the same Hausdorff dimension may have very different characteristics, for example, a straight line segment in ℝ2 and the Cartesian product in ℝ2 of two suitably chosen Cantor sets in ℝ will both have Hausdorff dimension 1. In this paper we develop a measure-theoretic method of distinguishing between the sets of such pairs.

MSC classification

Secondary: 28A75: Length, area, volume, other geometric measure theory
Type
Research Article
Information
Mathematika , Volume 35 , Issue 1 , June 1988 , pp. 1 - 27
Copyright
Copyright © University College London 1988

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