Admissible and singular translates of measures on vector spaces

Abstract

We provide a general setting for studying admissible and singular translates of measures on linear spaces. We apply our results to measures on D [ 0 , 1 ] D[0,1] . Further, we show that in many cases convex, balanced, bounded, and complete subsets of the admissible translates are compact. In addition, we generalize Sudakov’s theorem on the characterization of certain quasi-invariant sets to separable reflexive spaces which have the Central Limit Property.