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arXiv · 0707.3532

On the Hausdorff dimension of invariant measures of weakly contracting on average measurable IFS

Joanna Jaroszewska·Michal Rams
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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.

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Joanna Jaroszewska, Michal Rams. 2008-05-06. On the Hausdorff dimension of invariant measures of weakly contracting on average measurable IFS. https://doi.org/10.1007/s10955-008-9566-3

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