Geodesic
Continuous dependence on parameters of certain self-affine measures, and their singularity
Czechoslovak Mathematical Journal, Tome 61 (2011) no. 2, pp. 495-508.

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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.
DOI : 10.1007/s10587-011-0068-0
Classification : 28A80
Keywords: iterated function system; self-affine set; self-affine measure; singularity 
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     title = {Continuous dependence on parameters of certain self-affine measures, and their singularity},
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Ding, Daoxin. Continuous dependence on parameters of certain self-affine measures, and their singularity. Czechoslovak Mathematical Journal, Tome 61 (2011) no. 2, pp. 495-508. doi : 10.1007/s10587-011-0068-0. http://geodesic.mathdoc.fr/articles/10.1007/s10587-011-0068-0/

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