The dimension of projections of self-affine sets and measures
Abstract
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 = dimL mu, where dimH and dimL denote Hausdorff and Lyapunov dimensions, then the projection of mu in all but at most one direction has Hausdorff dimension mindimH mu,1. We transfer this result to sets and show that many self-affine sets have projections of dimension mindimH E,1 in all but at most one direction.
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