R^d上一个随机剪切集的Hausdorff维数

Hausdorff dimension of a random cut-out set in R^d

通过把随机集上的随机测度定义为与分形结构相关联的随机测度序列的极限,使用鞅方法讨论了Rd上一个随机剪切集的Hausdorff维数,获得直线上一个随机剪切集的Hausdorff维数结果在高维空间上的一个推广.

In this paper,we discuss Hausdorff dimension of a random cut-out set in Rd by using martingale techniques： the usual procedure is to define a random measure on the random set as the limit of a sequence of random measures associated with the construction,and to use martingales to deduce properties of the limiting measure,and to obtain a generalization of the results of a random cut-out set on the line.