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1 results

  • Visible parts of fractal percolation

  • Part of
  • Ida Arhosalo, Esa Järvenpää, Maarit Järvenpää, Michal Rams, Pablo Shmerkin
  • Journal:
    Proceedings of the Edinburgh Mathematical Society / Volume 55 / Issue 2 / June 2012
    Published online by Cambridge University Press:
    12 April 2012, pp. 311-331
    • Article
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  • We study dimensional properties of visible parts of fractal percolation in the plane. Provided that the dimension of the fractal percolation is at least 1, we show that, conditioned on non-extinction, almost surely all visible parts from lines are one dimensional. Furthermore, almost all of them have positive and finite Hausdorff measure. We also verify analogous results for visible parts from points. These results are motivated by an open problem on the dimensions of visible parts.