a1 The School of Mathematics, University of Bristol, University Walk, Bristol. BS8 1TW
If П is a k-dimensional vector subspace of Rn and E is a subset of Rn, let projп(E) denote the orthogonal projection of E onto П. Marstrand  and Kaufman  have developed results on the Hausdorff dimension and measure of projп(E) in terms of the dimension of E, leading to the very general theory of Mattila . In particular, Mattila shows that if the Hausdorff dimension dim E of the Souslin set E is greater than k, then projп(E) has positive k-dimensional Lebesgue measure for almost all П Gn, k (in the sense of the usual normalized invariant measure on the Grassmann manifold Gn, k of k-dimensional subspaces of Rn).
(Received April 01 1981)