关于自保形测度与 Lebesgue测度的等价性(英文)  

ON THE EQUIVALENCE OF SELF- CONFORMAL MEASURE TO LEBESGUE MEASURE

作　　者：张玉芹[1] 

机构地区：[1]武汉大学数学系,武汉430072

出　　处：《数学杂志》2001年第2期151-154,共4页Journal of Mathematics

基　　金：the Special Funds for Major State Basic Research Projects of China

摘　　要：本文我们研究了自保形测度与 Lebesgue测度的关系 ,对 Yuval Peres等的结果进行了推广 .证明了自相似测度要么是奇异的 ,要么关于 Lebesgue测度是绝对连续的 .并且若将 L ebesgue测度限制在自相似测度的紧支撑上 ,则其关于非奇异的自相似测度是绝对连续的 .In this article,we show that:the self-similar measure is either singular or absolutely continuous with respect to Lebesgue measure and the converse is true when Lebesgue measure is restricted to the compact support of the self-similar measure, which generalizes the result of Yuval Peres, etc., see[1].

关 键 词：自保形测度 LEBESGUE测度 开集条件 紧支撑 等价性 绝对连续 

分 类 号：O189.1[理学—数学]