向量值可测函数的连续性

Continuity of Vector-Valued Measurable Functions

本文给出了向量值可测函数等价类〔f〕的连续和弱连续的定义,并得到如下结果:如果〔f〕在〔a,b〕(?)R上(弱)连续,则必存在且唯一的g∈〔f〕使得g是〔a,b〕上的(弱)连续函数。以上定义及结论是A.C.Zaanen在文〔1〕中相应部分的推广。

Abstract In this paper, we will give the definitions of continuity and weak continuity of vector-valued measurable function equivalent class [f], and obtain the following results: If [f] is (weakly) contiunous on. [a, b](?)R, then there exists an unique function g∈[f] such that g is (weakly) continuous on [a, b]. These are generalizations of corresponding result of A. C. Zaanen[1].