Bibliographic Details
| Title: |
Absolute continuity of vector-valued self-affine measures |
| Authors: |
Deng, Qi-Rong1 dengfractal@126.com |
| Source: |
Journal of Mathematical Analysis & Applications. Jun2008, Vol. 342 Issue 2, p1250-1264. 15p. |
| Subjects: |
Absolute continuity, Boundary value problems, Measure theory, Vector analysis |
| Abstract: |
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. [Copyright &y& Elsevier] |
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| Database: |
Engineering Source |
