中文摘要：

Bylund和Gudayol（2000）指出,若紧度量空间X有有限的Assouad维数s和正的下Assouad维数t,则对任意s′〉s和0〈t’〈t，度量空间X上存在一个概率测度μ是上s’-齐性和下t＇-齐性的．他们在构造测度的过程中需要无限次的调整．本文用与WU（1998）对偶的方法给出一种比较简单和直观的证明．

英文摘要：

Bylund and Gudayol（2000） proved that if X is a compact metric space of finite Assouad dimension s and of positive Lower Assouad dimension t, then for any s′〉 s and t′〈 t, there is a probability measure μ on X, such that μ is upper s′-homogeneous and lower t′-homogeneous. Their proof is based on the construction of a measure that requires infinitely many adjustments. Using the method dual to WU（1998）, we give a simpler and more direct proof of their result.