| In this paper,we based on a paper《Vector Measures》of J.Diestl and J.Uhl.we promote several conclusion of vector measures valued in Banach space to locally convex space.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.Finally,we focus on promotion of some theorem in the reference[1],the promoted theorem as follows:Nikodym bounded theorem,Bartle-Dunford-Schwartz theorem,Diestel-Faires theorem,Orlicz-Pettis theorem,Vitali-Hahn-Saks-Nikodym theorem,Caratheodory-Hahn-Kluvanek extension theorem,Vitali-Hahn-Saks theorem,etc. |
