广义非均匀Cantor集的Hausdorff测度存在的充要条件的证明

摘要

The paper succeeds in the obtaining a class of generalized non-uniform Cantor set based on the iteration (1): Si(x) =aix + bi, x ∈[0,1], i = 1,2,…,m, where 0＜ai＜1,i=1, 2,…, m; bi + ai＞0, i = 1,2,…, m-1, b1=0 and am + bm = 1. Providing the sufficient and necessary conditions of its existence Hausdorff measure.