局部凸分离空间上的Caratheodory-Hahn-Kluvanek延拓定理  

Caratheodory-Hahn-Kluvanek Extentsion Theorem on Locally Convex Space

作　　者：乌仁其其格[1] 杨梅荣[1] WuRenQiQiGe;YANG Mei-rong(Department of Mathematics and Statistics, Chifeng University, Chifeng 024000, China)

机构地区：[1]内蒙古赤峰学院数学与统计学院

出　　处：《数学的实践与认识》2019年第10期262-267,共6页Mathematics in Practice and Theory

摘　　要：运用测度理论的方法将Banach空间上的Caratheodory-Hahn-Kluvanek延拓定理作进一步研究.首先在局部凸空间中引入P完备、分离等概念,并讨论P完备的局部凸分离空间上的Caratheodory-Hahn-Kluvanek延拓定理,进而给出Banach空间族的乘积空间上的Caratheodory-Hahn-Kluvanek延拓定理.Using the method of vector measure theory In Banach space, for further research the Caratheodory-Hahn-Kluvanek extentsion theorem On the locally convex space. First introduced the concept of P complete and separation in locally convex space. Research the Caratheodory-Hahn-Kluvanek extension theorem on p-completed locally convex separated space, further gives the Caratheodory-Hahn-Kluvanek extentsion theorem On the product space of Banach spaces.

关 键 词：局部凸空间 lcs空间 BANACH空间 乘积空间 Caratheodory-Hahn-Kluvanek延拓定理 

分 类 号：O177.2[理学—数学]