Translating the Cantor set by a random real - Dougherty, Randall; Lutz, Jack; Mauldin, R. Daniel; Teutsch, Jason (Transactions of the American Mathematical Society, 2014)
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-Löf 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 random Cantor set translate with a given constructive dimension.
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