Random recursive construction of self-similar fractal measures. The noncompact case
- Cite this article as:
- Arbeiter, M. Probab. Th. Rel. Fields (1991) 88: 497. doi:10.1007/BF01192554
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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 Falconer, Graf and Mauldin/Williams 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.