Hausdorff measures

For a fixed probability vector P=(p_0,p_1,…,p_ m-1)(m≥2),The Besicovitch set B is the set of points in the unit interval which contain j(0≤j≤m-1) in their madic expansions in the propotion p_j((0≤j≤m-1)); it is known that B has Hausodrff dimension-∑p_jlogp_jlogm, and its Hausdorff measures(under any gauge) are either zero or infinity.

给定一个概率向量P =(p0 ,p1,… ,pm -1) (m≥ 2 ) ,贝西科维奇集B由单位区间中那些在m 进制展开 ,式中j(0≤j≤m - 1)出现的频率为pj((0≤j≤m - 1) )的点组成 ,已经知道它在任何量纲下的豪斯道夫测度非零即无穷 本文运用测度的微扰法证明了西科维奇集的豪斯道夫测度为无穷大 。

Hausdorff dimension of sets of non differentiability points of some Cantor-type functions ;

一类康拓型函数不可微点集的豪斯道夫维数(英文)

In this paper,the discrete Hausdorff dimension problelli for isinvestigated.

设是ｄ维格子点上的严格α－稳定的随机游动，称为的Ｐ重点集（Ｐ１），本文讨论了的离散豪斯道夫维数，并对，（ａ＜ｄ），证明了Ｐ重点集的维数都等于ａ，

In this paper, we discuss the calculation method of Hausdorff dimension and box dimension for several special self-similar sets and obtain the corresponding results.

本文主要探讨几个特殊自相似集的豪斯道夫维数与盒维数的计算方法。