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Family of Strongly Additive Vector Measures

Xin-Lei Yong, Yi-Fan Han, Ling-Shan Xu, Yuan-Hong Tao

The family of strongly additive vector measures is characterized in this paper. Firstly, the sufficient and necessary condition of a vector measure, which takes values in a completely Hausdorff topological vector space, to be strongly addtive is established. Then BT B spaces are discussed and a Diestel-Faires type result is obtained.