关于一些自仿测度的绝对连续性和奇异性

摘要

奇异性是测度的一个重要性质,由定义得到某些自仿测度奇异的一个充分条件.借助于特征函数和测度的傅里叶变换,利用测度绝对连续性的定义,找到一类绝对连续的自仿测度,并对Li J-L的2个结论给出了简单的应用.%Singularity is an important property of measures. A sufficient condition on singularity of some self-affine measures is obtained by using the definition. A class of absolutely continuous self-affine measure is found by using Fourier transform and the definition of measure's absolute continuity. Some simple applications on two results of Li J-L are given.