距离空间上测度正则性的推广

An Extension of Measure Regularity in A Metric Space

本文给出了单调类与σ代数关系的充要条件,进一步得出距离空间的开集全体产生的最小单调类与产生的σ代数相等.利用这关系,证明了距离空间上的σ-有限测度也是正则测度.推广了距离空间上有限测度的正则性.

This paper gives a necessary and sufficient conditions form onotone class and σ algebra, and proves that the smallest monotone class stemming from all the open sets in a metric space is equivalent to the σ algebra. Finally, it proves that σ-finite measure in a metric space is regular, which extends the regularity of finite measure in a metric space.