Probability Theory and Related Fields

, Volume 88, Issue 4, pp 497-520

First online:

Random recursive construction of self-similar fractal measures. The noncompact case

  • Matthias ArbeiterAffiliated withSektion Mathematik, Friedrich-Schiller-Universität

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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.