The generalized purity law for ergodic measures: a simple proof
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...
We prove that in order to describe the Poisson boundary of rational affinities, it is necessary and sufficient to consider the action on real and all -adic fileds.