数字分配问题中测度与维数的研究

Rearch on the Problem of Measure and Dimension of Numerical Distribution

对于数字分配问题,将概率引入Cantor集中测度的相关问题,在其m进位制展开式的数字分配中,结合Hausdorff测度的性质和覆盖引理,推导出Hausdorff维数的一种有效的计算方法,这对于分形几何理论研究和分形曲线的性质的研究具有重要的作用.

The theory of measure and dimension of numerical distribution is an important content of fractal and geometry, which plays a role in researching on fractal properties. In this paper, probability is used in the problem of measure of Cantor set, in the numerical distribution of its - decimal expression, and a new effective solving formula of Hausdorff dimension is given by combining the character of Hausdorff measure.