UC Irvine

For a compact set K⊂ℝ1 and a family {Cλ}λϵJ of dynamically defined Cantor sets sufficiently close to affine with dimH K + dimH Cλ > 1 for all λ ϵ J, under natural technical conditions we prove that the sum K+C\ has positive Lebesgue measure for almost all values of the parameter λ. As a corollary, we show that generically the sum of two affine Cantor sets has positive Lebesgue measure provided the sum of their Hausdorff dimensions is greater than 1.