Translating the Cantor set by a random
  We determine the constructive dimension of points in random translates of the Cantor set. The Cantor set "cancels randomness" in the sense that some of its members, when added to Martin-Lof random reals, identify a point with lower constructive dimension than the random itself. In particular, we find the Hausdorff dimension of the set of points in a Cantor set translate with a given constructive dimension. 
Randall Dougherty, Jack Lutz, R. Daniel Mauldin, and Jason Teutsch
cs.CC