Random recursive constructions: asymptotic geometric and topological properties

  title={Random recursive constructions: asymptotic geometric and topological properties},
  author={R. Daniel Mauldin and S. C. Williams},
  journal={Transactions of the American Mathematical Society},
We study some notions of "random recursive constructions" in Euclidean m-space which lead almost surely to a particular type of topological object; e.g., Cantor set, Sierpiriski curve or Menger curve. We demonstrate that associated with each such construction is a "universal" number a such that almost surely the random object has Hausdorff dimension a. This number is the expected value of the sum of some ratios which in the deterministic case yields Moran's formula. We introduce the notion of a… 
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