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Box and packing dimensions of projections and dimension profiles

Published online by Cambridge University Press:  01 March 2001

J. D. HOWROYD
J. D. HOWROYD
Affiliation:
Department of Mathematics, Goldsmiths College, University of London, New Cross, London, SE14 6NW
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Abstract

For E a subset of ℝn and s ∈ [0, n] we define upper and lower box dimension profiles, B-dimsE and B-dimsE respectively, that are closely related to the box dimensions of the orthogonal projections of E onto subspaces of ℝn. In particular, the projection of E onto almost all m-dimensional subspaces has upper box dimension B-dimmE and lower box dimension B-dimmE. By defining a packing type measure with respect to s-dimensional kernels we are able to establish the connection to an analogous packing dimension theory.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 130 , Issue 1 , January 2001 , pp. 135 - 160
Copyright
2001 Cambridge Philosophical Society

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