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A Note on Hausdorff Measures of Quasi-Self-Similar Sets

A Note on Hausdorff Measures of Quasi-Self-Similar Sets

Sullivan has demonstrated that quasi-self-similarity provides a useful point of view for the study of expanding dynamical systems. In [4, p. 57] he posed the question: Is the Hausdorff measure of a quasi-self-similar set positive and finite in its Hausdorff dimension? This paper answers both parts of this question. In …