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Transactions of the American Mathematical Society

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Admissible and singular translates of measures on vector spaces

Authors: Alan Gleit and Joel Zinn
Journal: Trans. Amer. Math. Soc. 221 (1976), 199-211
MSC: Primary 60B05; Secondary 28A40, 60G30
MathSciNet review: 0436244
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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]$. 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.

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Keywords: Admissible translates, singular translates, Skorokhod topology on $ D[0,1]$, measures on vector spaces, quasi-invariant sets
Article copyright: © Copyright 1976 American Mathematical Society