Absolute continuity of vector-valued self-affine measures (Q2481922)

The author extends the definition of weak separation condition to self-affine IFS and gives necessary and sufficient conditions for vector-valued self-affine measures to be absolutely continuous with respect to Lebesgue measure. Then, the author proves that an absolutely continuous self-affine (scalar-valued) measure is equivalent to the restriction of the Lebesgue measure on the attractor. Finally, the author considers the invariant measure on the boundary of any invariant open set.