含参变量Cantor集的Hausdorff测度

THE HAUSDORFF MEASURE OF A CLASS OF CANTOR SET WITH PARAMETER

本文研究了菱形为基本集所构成的的广义Cantor集的Hausdorff测度问题.利用菱形几何结构的相关证明方法,获得了此类广义Cantor集的Hausdorff测度准确值,推广了曾超益和许绍元等人的已有结果.

This paper studies the problem of Hausdorff measure of a class of generalized Cantor sets constructed through the basic set diamond. By using geometric construction about diamond, we obtain the exact value of the Hausdorff measure of this generalized Cantor set, which extends Zeng and Xu’s results.