preparation

then introduced some new concept,for example:P-completed locally convex space、λ-absolutely continuous of vector measures for scalar valued measures、Bartle integral on locally convex space,etc.

引出了P-完备局部凸空间、向量测度关于纯量测度族λ的绝对连续性、局部凸空间上的Bartle积分等概念;重点推广了文献[1]中的如下定理:Nikodym有界定理、Bartle-Dunford-Schwartz定理、Pettis定理、Diestel-Faires定理、Orlicz-Pettis定理、Vitali-Hahn-Saks-Nikodym定理、Caratheodory-Hahn-Kluvanek延拓定理、Vitali-Hahn-Saks定理等。