概率空间上的盒维数  

Box dimension in a probability space

作　　者：李月玲[1] 

机构地区：[1]江苏师范大学数学与统计学院,江苏徐州221116

出　　处：《江苏师范大学学报（自然科学版）》2012年第4期29-33,共5页Journal of Jiangsu Normal University：Natural Science Edition

摘　　要：在概率空间(Ω,F,μ)上定义关于μ的上、下盒维数,并给出了上、下盒维数的另一等价定义,讨论了概率空间上关于μ的上、下盒维数与关于μ的Hausdorff维数、预填充维数及填充维数之间的关系.Let {X,, nE N} be a stochastic process on a probability space （Ω,F,μ）. Firstly, the upper and lower box dimension with respect to μ in a probability space are defined, then the equivalent definitions of the upper and lower box dimensions are given. At last, the relations are investigated between the upper and lower box dimensions with respect to μ and Hausdorff dimension, pre-packing and packing dimension with respect to p.

关 键 词：盒维数 HAUSDORFF维数 测度 填充维数 

分 类 号：O211.6[理学—概率论与数理统计]