# Hausdorff dimension in graph directed constructions

@article{Mauldin1988HausdorffDI, title={Hausdorff dimension in graph directed constructions}, author={R. Daniel Mauldin and S. C. Williams}, journal={Transactions of the American Mathematical Society}, year={1988}, volume={309}, pages={811-829} }

We introduce the notion of geometric constructions in Rm governed by a directed graph G and by similarity ratios which are labelled with the edges of this graph. For each such construction, we calculate a number a which is the Hausdorff dimension of the object constructed from a realization of the construction. The measure of the object with respect to fl"* is always positive and <r-finite. Whether the ^""-measure of the object is finite depends on the order structure of the strongly connected…

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