Bulletin of the
Korean Mathematical Society BKMS

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 $\{A_j\}\subseteq \Sigma$.

Keywords: vector measure, strong boundedness, semivariation

MSC numbers: 46A05