一类非齐次Moran集的Hausdorff测度  

Hausdorff Measure of a Kind of Non-Homogeous Moran Set

作　　者：金艳玲[1] 魏毅强[2] 

机构地区：[1]山西大学商务学院,山西太原030031 [2]太原理工大学理学院,山西太原030024

出　　处：《中北大学学报（自然科学版）》2011年第1期63-66,共4页Journal of North University of China(Natural Science Edition)

摘　　要：利用质量分布原理与自然覆盖,对一类满足强分离条件的非齐次Moran集的Hausdorff测度进行了研究.证明了主要结论:对于由({nk}k≥1,{Φk}k≥1,{mk}k≥1)确定的非齐次Moran集E,它的s维Hausdorff测度是各同级相似比ci,j的s次幂的和,随i从1到k作乘积,并求当压缩次数k趋于无穷大时的乘积的极限值.With the mass distribution theory and natural cover,the paper studied a kind of Hausedorff measure of non-homogeneous Moran sets which satisfy the strong separation condition,and proved the following conclusions： for the non-homogeneous Moran sets E determined by（{nk}k≥1,{Φk}k≥1,{mk}k≥1）,its s dimension Hausedorff measure is got by multiplying the sum of s powers of the same level ratio ci,j from 1 to k according to i.The limit is also derived on the condition that k,the times of compression,tends to ∞.

关 键 词：MORAN集 HAUSDORFF测度 质量分布原理 

分 类 号：O174.1[理学—数学]