  Let $\{S_i\}_{i\in \Lambda}$ be a finite contracting affine iterated function
system (IFS) on ${\Bbb R}^d$. Let $(\Sigma,\sigma)$ denote the two-sided full
shift over the alphabet $\Lambda$, and $\pi:\Sigma\to {\Bbb R}^d$ be the coding
map associated with the IFS. We prove that the projection of an ergodic
$\sigma$-invariant measure on $\Sigma$ under $\pi$ is always exact dimensional,
and its Hausdorff 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.
