Packing dimensions of projections and dimension profiles

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Abstract

For E a subset of R(n) and 0 less than or equal to m less than or equal to n we define a 'family of dimensions' Dim(m)E, closely related to the packing dimension off, with the property that the orthogonal projection of E onto almost all m-dimensional subspaces has packing dimension Dim(m)E. In particular the packing dimension of almost all such projections must be equal. We obtain similar results for the packing dimension of the projections of measures. We are led to think of Dim(m)E for m is an element of [0, n] as a 'dimension profile' that reflects a variety of geometrical properties of E, and we characterize the dimension profiles that are obtainable in this way.

Original languageEnglish
Pages (from-to)269-286
Number of pages18
JournalMathematical Proceedings of the Cambridge Philosophical Society
Volume121
Publication statusPublished - Mar 1997

Keywords

  • SETS

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