Abstract
We have studied statistically self-similar measures together with statistically self-similar sets in this paper. A special kind of statistically self-similar measures has been constructed and a class of statistically self-similar sets as well.
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References
Hutchinson J E. Fractals and self-similarity.Indiana Univ Math J, 1981,30:713–747
Graf S. Statistically self-similar fractals.Prob Th Rel Fields, 1987,74:357–392
Falconer K J. The multifractal spectrum of statistically self-similar measures.J Theoretical Probability, 1994,7:681–702
Mauldin R D, Williams S C. Random recursive constructions: asymptotic geometric and topological properties.Tran Amer Math Soc, 1986,295:325–346
Hu Diheet al. An introduction to random fractals. Wuhan: Wuhan Univ Press, 1996
Gral S, Mauldin R D, Williams S C. The exact Hausdorff dimension in random recursive constructions.Memoirs Amer Math Soc, 1988,38:1–121
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Supported by the National Natural Science Fundation and the Doctral Programme Fundation of China
Hu Dihe: born in May 1935, Professor
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Dihe, H. The construction of statistically self-similar measures. Wuhan Univ. J. Nat. Sci. 2, 19–24 (1997). https://doi.org/10.1007/BF02834907
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DOI: https://doi.org/10.1007/BF02834907