Geodesic
The Lévy continuity theorem for nuclear groups
Studia Mathematica, Tome 136 (1999) no. 2, pp. 183-196 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Let G be an abelian topological group. The Lévy continuity theorem says that if G is an LCA group, then it has the following property (PL) a sequence of Radon probability measures on G is weakly convergent to a Radon probability measure μ if and only if the corresponding sequence of Fourier transforms is pointwise convergent to the Fourier transform of μ. Boulicaut [Bo] proved that every nuclear locally convex space G has the property (PL). In this paper we prove that the property (PL) is inherited by nuclear groups, a variety of abelian topological groups containing LCA groups and nuclear locally convex spaces, introduced in [B1].
DOI : 10.4064/sm-136-2-183-196
Keywords: Lévy continuity theorem, convergence of probability measures, nuclear groups 
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W. Banaszczyk. The Lévy continuity theorem for nuclear groups. Studia Mathematica, Tome 136 (1999) no. 2, pp. 183-196. doi: 10.4064/sm-136-2-183-196

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