中文摘要：

考虑了单位圆T=R/Z上的随机区间In（w）=wn＋（-ln/2;ln/2）（mod1），其中{ln}n≥1为一列单调下降并趋于0的正实数，{wn}n≥1为T上的一列独立同分布且具有Gibbs分布测度的随机变量．借助于重分形分析中的工具，估计了被随机区间序列{In（w））有限次覆盖以及无穷多次覆盖的集合的Hausdorff维数．

英文摘要：

We consider the random intervalsIn（w）=wn＋（-ln/2;ln/2）（mod1）（mod 1）, where {in}n〉_1 is a sequence of positive real numbers which is decreasing to zero and {ln}n≥1 is an i.i.d, sequence with Gibbs distribution measure on the circle {wn}n≥1 Using the tools from multi-fractal analysis, we estimate the Hausdorff dimension of sets which are covered finitely or infinitely many times by {In（w）}.