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The necessary and sufficient conditions for various self-similar sets and their dimension. (English) Zbl 1047.60028

Summary: We give several necessary and sufficient conditions for statistically self-similar sets and a.s. self-similar sets and get the Hausdorff dimension and exact Hausdorff measure function of any a.s.self-similar set. It is useful in the study of probability properties and fractal properties and structure of statistically recursive sets.

MSC:

60G10 Stationary stochastic processes
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References:

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