Some remarks on the Hausdorff measure of the Cantor set

Abstract

In this paper, the author further reveals some intrinsic properties of the Cantor set. By the properties, the author gives a new method for calculating the exact value of the Hausdorff measure of the Cantor set, and shows the facts that each covering which consists of basic intervals, in which any basic interval cannot completely contain the other, is the best covering of the Cantor set, and the Hausdorff measure of the Cantor set can be determined by coverings which only consist of basic intervals.

Keywords

• fractal
• Hausdorff measure
• Cantor set