自相似集的质量分布原理与Hausdorff测度及其应用

On the Mass Distribution Principle and Hausdorff Measure for the Self-Similar Sets and Applications

本文提出了满足开集条件的自相似集的质量分布原理.作为应用,得到了计算一类满足开集条件的自相似集的Hausdorff测度的准确值的方法,并举例说明了此方法对于计算一类满足开集条件的自相似集的Hausdorff测度的准确值是行之有效的.

In this paper, the mass distribution principle for the self-similar sets satisfying the open set condition （OSC） is set up. As an application, we obtain a new method for computing the exact value of the Hausdorff measure for a class of self-similar sets satisfying OSC. In addition, we give two examples to show that the new method is effective and workable to compute the exact values of the Hausdorff measures of a class of self-similar sets satisfying OSC.