Multifractal decomposition of statistically self-similar sets. (Chinese. English summary) Zbl 1037.60040

Yu, Jinghu; Hu, Dihe

Acta Math. Sin. 46, No. 3, 507-512 (2003).

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

Keywords:

statistically self-similar sets; multifractal decomposition; spectrum function