Let {SiIi2 integral be a finite contracting affine iterated function system (IFS) on Rd. Let (E, a) denote the two-sided full shift over the alphabet A, and let n : E ! Rd be the coding map associated with the IFS. We prove that the projection of an ergodic a-invariant measure on E under n is always exact dimensional, and its Haus-dorff dimension satisfies a Ledrappier-Young-type formula. Furthermore, the result extends to average contracting affine IFSs. This completes several previous results and answers a folklore open question in the community of fractals. Some applications are given to the dimension of self-affine sets and measures.
展开▼
