Random coverings of thin sets (Q1081951)

Let E be a bounded set in \(R^ d\) and consider covering E by a random collection of small sets. In this paper the small sets are cubes of fixed size with edges parallel to the coordinate axes and independent uniformly distributed centres. E is a (infinite) thin set such as fractal curves or Cantor sets. Let \(N_ a\) be the number of cubes of size a \((=length\) of edge) required to cover E. Results are obtained concerning different problems related to the behaviour of \(N_ a\) as \(a\to 0\).