This thesis wes based on the monograph《 Vector Measures》 of J. Diestel,J. J. Uhl,complementing and improving some work in the literature [ 2 ]. We discussed the Caratheodory - Hahn extension theorem in separated locally convex space.%以J.Diestel和J.J.Uhl的名著《Vector Measures》为基础,将Banach空间中的Caratheodory-Hahn延拓定理推广到了局部凸分离空间.
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