关于m+1分非均匀Cantor集的Hausdorff测度的充分必要条件

The Necessary and Sufficient Conitions on the Hausdorff Measure of m + 1 Non-uniform Cantor Set

本文考虑由一类线性迭代系统产生的多分非均匀Cantor集,讨论了这类非均匀Cantor集的几何结构,获得了相关的性质,给出了这类多分非均匀Cantor集Hausdorff测度的一个充分必要条件。

We consider a multiple non-uniform Cantor set which is constructed by a linear iterated system, obtain some properties about the set. Presented are also some necessary and sufficient conditions for the Hausdorff measure of m non-uniform Cantor set.