一类Cantor型集合交的分形结构

FRACTAL STRUCTURE OF SOME CANTOR INTERSECT SETS

通过对一类Cantor型集合交的结构的分析 ,获得了不同位置的Cantor型集合交的Hausdorff测度之间的关系 ,并进一步验证了关于它的维数公式 。

This paper studies the fractal structure of some Cantor intersect sets and get the relations of the Hausdorff measure between two Cantor intersect sets.Their Hausdorff dimension formula is also proved by a new method. Meanwhile the better upper bound of the Hausdorff measure is obtained.