Mathematical Proceedings of the Cambridge Philosophical Society

Box and packing dimensions of projections and dimension profiles

a1 Department of Mathematics, Goldsmiths College, University of London, New Cross, London, SE14 6NW


For E a subset of [open face R]n and s [set membership] [0, n] we define upper and lower box dimension profiles, B-dims E and B-dims E respectively, that are closely related to the box dimensions of the orthogonal projections of E onto subspaces of [open face R]n. In particular, the projection of E onto almost all m-dimensional subspaces has upper box dimension B-dimm E and lower box dimension B-dimm E. 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.

(Received October 6 1999)
(Revised May 22 2000)