Singularity of certain self-affine measures

Abstract: The self-affine measure associated with an iterated function system and a weight is uniquely determined. The problem of determining whether a self-affine measure is absolutely continuous or singular has been studied extensively in recent years. In the present paper we consider the singularity of certain self-affine measures. We obtain a sufficient condition for such measures being singular. Two applications of this result are given, which extend several known results in a simple manner. [Copyright &y& Elsevier]