摘要
得到了 Ｈａｕｓｄｏｒｆｆ容度与 Ｈａｕｓｄｏｒｆｆ测度相等的集的充分必要条件．对于满足开集条件的自相似集，验证了它的Ｈａｕｓｄｏｒｆｆ容度与Ｈａｕｓｄｏｒｆ测度相等并给出了它的Ｈａｕｓｄｏｒｆｆ测度的一个便于应用的公式．作为例子，给出了均匀康托集的Ｈａｕｓｄｏｒｆｆ测度的一种新的计算方法，对于Ｋｏｃｈ曲线的Ｈａｕｓｄｏｒｆｆ测度的上限也作了讨论．
Some sufficient and necessary conditions for sets having the same Hausdorff content and Hausdorff measure are obtained. For the self-similar set satisfying the open set condition, it is proved that its Hausdorff content and Hausdorff measure are equal and a formula, which is convenient for use, of its Hausdorff measure is given. As applications, the Hausdorff measures of uniform Cantor sets are computed in a new way and the upper bound problem of the Hausdorff measure of the Koch curve is also discussed.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2001年第1期117-124,共8页
Acta Mathematica Sinica：Chinese Series
基金
淮北煤炭师范学院及韩山师范学院科研基金资助项目。
关键词
容度
测度
维数
开集条件
自相似集
Content
Measure
Dimension
Open set condition
Self-similar sets
