On the nuclearity of a dual space with the convergence in probability topology

  • S. Kwapien
  • W. Smolenski


Let μ be a probability measure on a separable locally convex Fréchet space E and let sμ denote the topology on E′ of the convergence in μ. Then (E′, sμ) is nuclear iff μ((E', sμ))=1.


Stochastic Process Probability Measure Probability Theory Mathematical Biology Dual Space 
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Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • S. Kwapien
    • 1
  • W. Smolenski
    • 2
    • 3
  1. 1.Institute of MathematicsWarsaw UniversityWarsawPoland
  2. 2.Dept. of MathematicsLousiana State UniversityBaton Rouge
  3. 3.Institute of MathematicsWarsaw Technical UniversityWarsawPoland

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