取值于局部凸空间中抽象集函数的积分

Integrals of Set-Functions Valued in Locally Convex Spaces

本文讨论定义于紧Hausdorff空间而取值于局部凸空间中抽象函数的几种积分及其它们之间的相互关系,这些积分是抽象函数Riemann积分的一般化,作为应用,给出了几类重要局部凸空间的新特征。

In this paper, several kinds of set-functions integration valued in locally convex spaces, defined in a compact Hausdorff space are defined. The relationships among them are discussed and as a result the definition and existent condition of some kind of Riemann integral of abstract function valued in locally convex spaces arc given. At last, some kinds of important locally convex spaces are described.