用随机小区间覆盖圆周(英文)

COVERING THE CIRCLE WITH SMALL RANDOM INTERVALS

本文考虑随机区间I_n=ω_n+(- e_n/2,e_n/2)(mod 1).利用文献[7]中所介绍的无处不在系统,证明了圆周上由被无穷次覆盖的点构成的集合的Hausdorff数几乎必然等于min{1,■},推广了文献[4]中的结果.

In this article,we consider the random intervals I_n =ω_n ＋（- e_n/2,e_n/2）（mod 1）. By using ubiquitous system which was introduced in[7],we prove that the Hausdorff dimension of the set of points covered infinitely often is almost surely equal to min{1,■ log n/-log e_n },which generalizes an earlier result of Fan and Wu[4].