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We study families of possibly overlapping self-affine sets. Our main example is a family that can be considered the self-affine version of Bernoulli convolutions and was studied, in the non-overlapping case, by F.Przytycki and M.Urbański [PU89]. We extend their results to the overlapping region and also consider some extensions and generalizations. 1
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Pablo Shmerkin (2006) studied this question.
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