A Kronecker-Weyl Theorem from Interpolation Sets

Abstract

An analog of the classical Kronecker-Weyl theorem for weak uniform distribution is obtained for an arbitrary countably infinite independent subset of a discrete abelian group using a type of interpolation sets called epsilon-Kronecker sets. Specifically, the topological size of the set of homomorphisms inducing weakly uniformly distributed sequences is established by showing that it forms a dense G-delta set.