The Lévy continuity theorem for nuclear groups

Volume 136 / 1999

W. Banaszczyk Studia Mathematica 136 (1999), 183-196 DOI: 10.4064/sm-136-2-183-196

Abstract

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].

Authors

  • W. Banaszczyk

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