正规测度的一个特征

A Characterization of Normal Measures

利用紧Ｈａｕｓｄｏｒｆ空间Ｘ中闭无处稠子集与连续函数空间Ｃ（Ｘ）中单调网之间的对应关系，得到正规测度的一个特征：定理设Ｘ是紧Ｈａｕｓｄｏｒｆ空间，则０≤μ∈Ｍ（Ｘ）是正规的当且仅当对Ｘ中的每一闭无处稠子集Ｇ。

By applying the corresponding relation of the monotonic nets of the continuous function space C(X) on a compact Hausdorff space X and the closed nowhere dense subsets of X, it was obtained in this note a characterization of normal measures.Theorem Let X be a compact Hausdorff space , a regular measure μ∈ M(X) is normal if and only if for each closed nowhere dense set G in X , [(-μ)∨μ]( G )=0