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The necessary and sufficient conditions for various self-similar sets and their dimension
Authors:Dihe Hu
Affiliation:College of Mathematical Science, Wuhan University, Wuhan, 430072, People's Republic of China
Abstract:We have given several necessary and sufficient conditions for statistically self-similar sets and a.s. self-similar sets and have got the Hausdorff dimension and exact Hausdorff measure function of any a.s. self-similar set in this paper. It is useful in the study of probability properties and fractal properties and structure of statistically recursive sets.
Keywords:Statistically self-similar sets   A.s. self-similar sets   Hausdorff dimension   Statistically recursive sets   Statistical contraction operators
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