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The probability character of statistically self-similar sets and measures. (Chinese. English summary) Zbl 1039.28010

Summary: We prove that a statistically self-similar set is generated by a collection of random contraction operators \(\{f_\sigma\), \(\sigma \in D\}\), where \(f_\sigma\) is a random element from a probability space \((\Omega,{\mathcal F},P)\) to \(\text{con} (E)\), where \(\text{con} (E)\) denotes all contraction operators from a complete separable metric space \(E\) into itself.

MSC:

28A80 Fractals
60G18 Self-similar stochastic processes
60D05 Geometric probability and stochastic geometry
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