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ArticleOriginal scientific text

Title

The Lévy continuity theorem for nuclear groups

Authors 1

Affiliations

  1. Faculty of Mathematics, Łódź University, Banacha 22, 90-238 Łódź, Poland

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].

Keywords

ENG
Lévy continuity theorem, convergence of probability measures, nuclear groups

Bibliography

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Studia Mathematica
1999/136/2
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Pages:
183-196
Main language of publication
English
Received
1999-01-11
Accepted
1999-04-14
Published
1999
Exact and natural sciences