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manuscripta mathematica

, Volume 39, Issue 2–3, pp 147–153 | Cite as

A space of vector-valued measures and a strict topology

  • Jafar Zafarani
Article

Abstract

Let X be a completely regular Hausdorff space and let E be a real locally convex Hausdorff space. Katsaras [2] has studied the topologies β0, β, and β1, for the vector-valued case on Crc(X,E), the space of all continuous E-valued functions on X with relatively compact range. The corresponding dual spaces are the spaces Mt (B,E'), Mτ (B,E'), and M (B,E') of all t-additive, all τ-additive, and all σ-additive members of M(B,E'), the dual space of Crc (X,E') under the uniform topology. In this paper we study the subspace Me(B,E') of M(B,E'). A locally convex topology βe is defined on Crc(X,E) that yields Me (B,E') as a dual space. It is proved that if E is strongly Mackey then (C (X,E),βe) is strongly Mackey.

Keywords

Dual Space Hausdorff Space Uniform Topology Convex Topology Continuous Seminorm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Jafar Zafarani
    • 1
  1. 1.Department of MathematicsUniversity of IsfahanIsfahanIran

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