中文摘要：

考虑单位立方体内生成的一类自相似集的Hausdorff测度的计算问题,在相似比满足一定条件下,证明了自然覆盖为实现上凸密度1的最好形状,即自然覆盖为最好覆盖.作为推论,得到该类自相似集的Hausdorff测度的精确值为（√3）s,其中s为Hausdorff维数.

英文摘要：

The problem of calculation of Hausdorff measures of a class of self-similar sets in a regular hexahe- dron was studied in this paper When the similitude ratios satisfied certain conditions,it was proved that the natural cover was the best shape for upper convex density It means that the natural cover was a best one As a result, the ex- act value of Hausdorff measure of this class of self-similar sets is （√3）s,where s is Hausdorff dimension.