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Projection theorems for box and packing dimensions

Published online by Cambridge University Press:  24 October 2008

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

We show that if E is an analytic subset of ℝn then

for almost all m–dimensional subspaces V of ℝn, where projvE is the orthogonal projection of E onto V and dimp denotes packing dimension. The same inequality holds for lower and upper box counting dimensions, and these inequalities are the best possible ones.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 119 , Issue 2 , February 1996 , pp. 287 - 295
Copyright
Copyright © Cambridge Philosophical Society 1996

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References

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