On the Hausdorff dimension of invariant measures of weakly contracting on average measurable IFS
arXiv:0707.3532 · doi:10.1007/s10955-008-9566-3
Abstract
We consider measures which are invariant under a measurable iterated function system with positive, place-dependent probabilities in a separable metric space. We provide an upper bound of the Hausdorff dimension of such a measure if it is ergodic. We also prove that it is ergodic iff the related skew product is.
16 pages; to appear in Journal of Stat. Phys