THE DIMENSION OF PROJECTIONS OF SELF-AFFINE SETS AND MEASURES

Let E be a plane self-affine set defined by affine transformations with linear parts given by matrices with positive entries. We show that if mu, is a Bernoulli measure on E with dimH mu = dim(L) mu, where dim(H) and dim(L), denote Hausdorff and Lyapunov dimensions, then the projection of mu in all but at most one direction has Hausdorff dimension min{dim(H), mu, 1}. We transfer this result to sets and show that many self-affine sets have projections of dimension min{dim(H) E, 1} in all but at most one direction.