  We study probabilistic iterated function systems (IFS), consisting of a
finite or infinite number of average-contracting bi-Lipschitz maps on R^d. If
our strong open set condition is also satisfied, we show that both upper and
lower bounds for the Hausdorff and packing dimensions of the invariant measure
can be found. Both bounds take on the familiar form of ratio of entropy to the
Lyapunov exponent.
