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On Hausdorff and packing dimension of product spaces

Published online by Cambridge University Press:  24 October 2008

J. D. Howroyd
J. D. Howroyd
Affiliation:
Mathematical Institute, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS
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Abstract

We show that for arbitrary metric spaces X and Y the following dimension inequalities hold:

where ‘dim’ denotes Hausdorff dimension and ‘Dim’ denotes packing dimension. The main idea of the proof is to use modified constructions of the Hausdorff and packing measure to deduce appropriate inequalities for the measure of X × Y.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 119 , Issue 4 , May 1996 , pp. 715 - 727
Copyright
Copyright © Cambridge Philosophical Society 1996

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