上凸密度与Hausdorff测度——满足开集条件的自相似集

The Upper Convex Density and Hausdorff Measure——The Self-similar Set Satisfying OSC

对于满足开集条件的自相似集E ,证明关于上凸密度的一个实现定理 ,即证明存在U ,满足 ｜U｜>0 ,使得H2 (E∩U) ｜U｜s =1。作为应用给出计算这类分形的Hausdorff测度的一个表达式。最后提出某些问题和猜测。

For a self_similar set E satisfying OSC, a realization on the upper convex density is proved, that is, there is U with |U|>0 such that H s(E∩U)/|U| s=1, and as its application, a formula for the calculation of the Hausdorff meaure of E is obtained. Some problems and conjectures are also proposed.