Bull. Korean Math. Soc. 2000 Vol. 37, No. 2, 209-215

Li Ronglu and Shin Min Kang Harbin Institute of Technology, Gyeongsang National University

Abstract : Let $X$ be a locally convex space. A series of clearcut characterizations for the boundedness of vector measure $\mu :\Sigma \to X$ is obtained, e.g., $\mu$ is bounded if and only if $\mu(A_j)\to 0$ weakly for every disjoint $\{A_j\}\subseteq \Sigma$ and if and only if $\big\{{1\over {j^j}}\mu(A_j)\big\}_{j=1}^\infty$ is bounded for every disjoint $\{A_j\}\subseteq \Sigma$.