一类集合的 MINKOWSKI 容度

THE MINKOWSKI CONTENT OF A CLASS OF SETS

本文对区间[0,1]中的可列点集的 Minkowski 容度进行了系统的研究,确定了可列点集的 Minkowski 容度为正有限、0或+∞的条件,并且还确定了它们的 Bouligand 维数。

In this paper,we study systematically the Minkowski contents of countablesubsets of the interval[0,1].We determine completely the conditions suchthat the Minkowski contents of these sets are positively finite,null orinfinite.We determine also their Bouligand dimensions.