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].
@article{bwmeta1.element.bwnjournal-article-smv136i2p183bwm,
author = {W. Banaszczyk},
title = {The L\'evy continuity theorem for nuclear groups},
journal = {Studia Mathematica},
volume = {133},
year = {1999},
pages = {183-196},
zbl = {0940.43001},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv136i2p183bwm}
}
Banaszczyk, W. The Lévy continuity theorem for nuclear groups. Studia Mathematica, Tome 133 (1999) pp. 183-196. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv136i2p183bwm/
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