关于某些自仿测度的奇异性

On the Singularity of Certain Self-affine Measures

自仿测度与迭代函数系和权相关联,并且被唯一地确定。近年来,关于自仿测度是绝对连续或奇异的问题已经得到广泛研究。主要考虑某些自仿测度的奇异性,给出它们奇异性的一个充分条件,及其相应的应用。

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 and give a sufficient condition for such measures being singular and its application.