Summary
Let μ be a probability measure on a separable locally convex Fréchet space E and let s μ denote the topology on E′ of the convergence in μ. Then (E′, s μ) is nuclear iff μ((E', s μ)′)=1.
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Kwapien, S., Smolenski, W. On the nuclearity of a dual space with the convergence in probability topology. Z. Wahrscheinlichkeitstheorie verw Gebiete 59, 197–201 (1982). https://doi.org/10.1007/BF00531743
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DOI: https://doi.org/10.1007/BF00531743