一个特殊自相似分形集的Hausdorff测度的下界估计  

Estimation of the lower bound of Hausdorff measure of a special self-similar fractal set

作　　者：李浩[1] 陈尔明[1] 

机构地区：[1]华侨大学数学系,福建泉州362021

出　　处：《福州大学学报（自然科学版）》2005年第5期562-564,共3页Journal of Fuzhou University(Natural Science Edition)

摘　　要：利用自相似分形的结构性质和质量分布原理,通过定义支撑在分形集上恰当的质量分布,具体地分析了直径在不同的分区内的可测集的直径大小与分布在其上的质量多少之间的关系,得到了一个由Falconer提出的特殊分形集Hausdorff测度的下界估计,HS(F)≥0.807 758 0.According to the property of serf-similar fractal and the theory of quality-distribution, by defining a right quality-distribution supporting on the fractal set, analyzing concretely the relation between diameters of measurable sets in various intervals and quality distributing on them, an upper bound of Hausdorff measure of a special fractal, which is introduced by Falconer, is obtained in this paper, H^s（F）≥0.8077580.

关 键 词：自相似 HAUSDORFF测度 质量分布 下界 

分 类 号：O174.12[理学—数学]