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The packing dimension of projections and sections of measures

Published online by Cambridge University Press:  24 October 2008

Kenneth J. Falconer  and
Pertti Mattila
Kenneth J. Falconer
Affiliation:
Mathematical Institute, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS, Scotland
Pertti Mattila
Affiliation:
Department of Mathematics, University of Jyväskylä, P.O. Box 35, FIN-40351 Jyväskylä, Finland
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Abstract

We show that for a probability measure μ on ℝn

for almost all m–dimensional subspaces V, provided dimH μ≤m. Here projv denotes orthogonal projection onto V, and dimH and dimp denote the Hausdorff and packing dimension of a measure. In the case dimH μ > m we show that at μ-almost all points x the slices of μ by almost all (n − m)-planes Vx through x satisfy

We give examples to show that these inequalities are sharp.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 119 , Issue 4 , May 1996 , pp. 695 - 713
Copyright
Copyright © Cambridge Philosophical Society 1996

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References

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