Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Projection theorems for box and packing dimensions

K. J. Falconera1 and J. D. Howroyda1

a1 Mathematical Institute, University of St. Andrews, North Haugh, St. Andrews, Fife KY16 9SS, Scotland

Abstract

We show that if E is an analytic subset of xs211Dn then

S0305004100074168_eqnU001

for almost all m–dimensional subspaces V of xs211Dn, 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.

(Received July 21 1994)