  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 dim_H 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.
