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. It is natural to expect that the arithmetic sum of two Cantor sets should have positiveLebesgue measure if the sum of their dimensions exceeds 1, but there are many known counterexamples,e.g. when both sets are the middle-ff Cantor set and ff 2 (13 ;12 ). We show that for anycompact set K and for a.e. ff 2 (0; 1), the arithmetic sum of K and the middle-ff Cantor set doesindeed have positive Lebesgue measure when the sum of their Hausdorff dimensions exceeds 1.In this case we also...

Self-similar measures and intersections of Cantor sets