Department of Mathematics, Goldsmiths College, University of London, New Cross, London, SE14 6NW
Published online: 01 March 2001
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.
2001 Cambridge Philosophical Society
Recommend this journal
Email your librarian or administrator to recommend adding this journal to your organisation's collection.
Mathematical Proceedings of the Cambridge Philosophical Society