Further Study For Vector Measures Valued In Locally Convex Space

This thesis was based on the monograph《Vector Measures》of J.Diestel and J.J.Uhl,complementing and improving some work in the literature.We extended several important results of vector measures valued in Banach spaces to separated locally convex spaces.The article discussed the Caratheodory-Hahn Extension Theorem in separated locally convex spaces;and proved that sequential completeness of P- complete locally convex space X which has the "lifting property" on the vector measure spaces sa(Σ,X),ca(Σ,X),bva(Σ,X),bvca(Σ,X).In view of the Stone Representation Theorem, we proved that sa(F,X) and ca(σ((?)),X),bva(F,X)and bvca(σ((?)),X)are both topological isomorphic in a product space of Banach spaces.At the and of the article,we got the Yosida-Hewitt Decomposition Theorem and Lebesgue Decomposition Theorem in a product space of Banach spaces.