Abstract
Let X be the quotient group of the S-adele ring of an algebraic number field by the discrete group of S-integers. Given a probability measure µ on X d and an endomorphism T of X d , we consider the relation between uniform distribution of the sequence T n x for µ-almost all x ∈ X d and the behavior of µ relative to the translations by some rational subgroups of X d . The main result of this note is an extension of the corresponding result for the d-dimensional torus T d due to B.Host.
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