Inserted: 13 aug 2007
Journal: Illinois Journal of Mathematics
We extend the well-known Moran-Hutchinson Theorem, saying that under the open set condition the Hausdorff dimension of self-similar sets coincides with the similarity dimension, to the more general setting of doubling metric spaces and prove its reverse implication. We also provide examples of iterated function systems in doubling metric spaces where our results apply.
Keywords: Hausdorff dimension, metric spaces, fractal sets