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.