Absolute continuity of vector-valued self-affine measures |
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Authors: | Qi-Rong Deng |
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Affiliation: | Department of Mathematics, Fujian Normal University, Fuzhou 350007, PR China |
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Abstract: | This paper is devoted to the absolute continuity of (scalar-valued or vector-valued) self-affine measures and their properties on the boundary of an invariant set. We first extend the definition of WSC to self-affine IFS, and then obtain a necessary and sufficient condition for the vector-valued self-affine measures to be absolutely continuous with respect to the Lebesgue measure. In addition, we prove that, for any IFS and any invariant open set V, the corresponding (scalar-valued or vector-valued) invariant measure is supported either in V or in ∂V. |
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Keywords: | Self-affine IFS Vector-valued measure Absolute continuity Lebesgue measure |
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