Weakly controlled Moran constructions and iterated functions systems in metric spaces

Tapio Rajala, Markku Vilppolainen
2011 Illinois Journal of Mathematics  
We study the Hausdorff measures of limit sets of weakly controlled Moran constructions in metric spaces. The separation of the construction pieces is closely related to the Hausdorff measure of the corresponding limit set. In particular, we investigate different separation conditions for semiconformal iterated function systems. Our work generalizes well known results on self-similar sets in metric spaces as well as results on controlled Moran constructions in Euclidean spaces.
doi:10.1215/ijm/1369841795 fatcat:gzjqf73zjbb2baldjdzmmz44ey