in this article, we determine the Hausdorff dimension of the comformal graphdirected set, prove that the associated Hausdorff measure is positive o-finite, and give the sufficient and necessary condition that makes Hausdorff measure be positive finite.
Hui XU.
The Hausdorff Dimension and Measure of Conformal Graph-Directed Sets. Acta Mathematica Sinica, Chinese Series, 2001, 44(4): 633-640 https://doi.org/10.12386/A2001sxxb0083