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  • Cited by 13
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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 119, Issue 2
  • February 1996, pp. 287-295

Projection theorems for box and packing dimensions

  • K. J. Falconer (a1) and J. D. Howroyd (a1)
  • DOI: http://dx.doi.org/10.1017/S0305004100074168
  • Published online: 24 October 2008
Abstract
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.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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