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Multifractal decomposition of statistically self-similar sets. (Chinese. English summary) Zbl 1037.60040
Summary: Let \(K\) be a statistically self-similar set defined by S. Graf [Probab. Theory Relat. Fields 74, 357–392 (1987; Zbl 0591.60005)]. We construct a random measure \(\rho\) which is supported by \(K\), and study the multifractal decomposition for \(K\) with \(\rho\). Under such a decomposition, we obtain the expression of the spectrum function \(f(\alpha)\).

MSC:
60G46 Martingales and classical analysis
28A80 Fractals
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