Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

Streszczenie

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].