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Keywords:
iterated function system; self-affine set; self-affine measure; singularity
iterated function system; self-affine set; self-affine measure; singularity
Summary:
In this paper, we first prove that the self-affine sets depend continuously on the expanding matrix and the digit set, and the corresponding self-affine measures with respect to the probability weight behave in much the same way. Moreover, we obtain some sufficient conditions for certain self-affine measures to be singular.
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