关于自相似集存在最好H^s-几乎处处闭集覆盖的一个新充分必要条件

A New Sufficient and Necessary Condition Under Which Aself-Similar Set Has a Best-a.e.-Closed-Set Covering

该文得到了自相似集存在最好Hs-几乎处处闭集覆盖的一个新充分必要条件,从而改进和推广了许绍元、李国祯在2004年的一个结果.作为应用,我们讨论了直线上的一个满足强分离开集条件的自相似集.

In this paper, a new sufficient and necessary condition for the existence of the best -a. e.-closed-set covering of the self-similar set is obtained. As a result, we improve and generalize a corresponding result which is obtained by Shaoyuan Xu and Guozhen Li in 2004. As apphcations, a self-similar set satisfying the strong separation open set condition, which is constructed on the real line is well discussed.