Probability Theory and Related Fields

, Volume 88, Issue 4, pp 497–520

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

  • Matthias Arbeiter

DOI: 10.1007/BF01192554

Cite this article as:
Arbeiter, M. Probab. Th. Rel. Fields (1991) 88: 497. doi:10.1007/BF01192554


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.

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Matthias Arbeiter
    • 1
  1. 1.Sektion MathematikFriedrich-Schiller-UniversitätJenaGermany

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