中文摘要：

何和刘首次研究了平面上向量值系数Rademacher级数水平集的交集.他们的结果基于5个模不超过l的向量和的估计.本文继续研究高维空间Rademacher级数及其水平集.如果向量维数大于2,何和刘所用的估计方法失效.当Rademacher级数值域在全空间稠密或者等于全空间时,我们用面罩函数来研究该问题,以此考虑水平集的Hausdorff维数.

英文摘要：

He and Liu initiated a study of the intersection of level sets of Rademacher series through the Rademacher series with vector-value coefficients.Their result based on an estimation about the sum of five vectors which are less than one in norm.In this paper,we continue such investigation.Since the estimation is invahd if the dimension of vectors is larger than 2,we use the mask of a vector instead of employing the estimation to discuss when the Rademacher range of a sequence is dense or equal to the whole space.We then apply this result to consider the Hausdorff dimension of level sets.