CHARACTERIZATIONS OF BOUNDED VECTOR MEASURES

  • Ronglu, Li (Department of Mathematics, Harbin Institute of Technology) ;
  • Kang, Shin-Min (Department of Mathematics, Gyeongsang National University)
  • Published : 2000.05.01

Abstract

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

Keywords

vector measure;strong boundedness;semivariation

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