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A multifractal formalism. (English) Zbl 0841.28012
This is a long and carefully written paper examining up to what extent rigorous arguments can be provided for the so-called multifractal theory. The mathematical theory is based on Hausdorff and packing measures and their dimension notions on metric spaces. The author studies global dimension functions as well as local dimension functions (called multifractal spectra) on the support of Borel probability measures. Special attention is paid to the multifractal analysis of graph directed self-similar and “cookie-cutter” measures. Open questions are stated. Remarks to forthcoming papers after submitting year 1992 are also given.

MSC:
28A80 Fractals
28A78 Hausdorff and packing measures
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