Random recursive construction of self-similar fractal measures. The noncompact case
The self-similarity of sets (measures) is often defined in a constructive way. In the present paper it will be shown that the random recursive construction model of \textit{K. J. Falconer} [Math. Proc. Camb. Philos. Soc. 100, 559-582 (1986; Zbl 0623.60020)], \textit{S. Graf} [Probab. Theory Relat. Fields 74, 357-392 (1987; Zbl 0591.60005)], and \textit{R. D. Mauldin} and \textit{S. C. Williams} [Trans. Am. Math. Soc. 295, 325-346 (1986; Zbl 0625.54047)] for (statistically) self-similar sets may be generalized to the noncompact case. We define a sequence of random finite measures, which converges almost surely to a self-similar random limit measure. Under certain conditions on the generating Lipschitz maps we determine the carrying dimension of the limit measure.
scientific article; zbMATH DE number 4192774
scientific article