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Ensembles normaux

Michel Mendès France (1968/1969)

Séminaire de théorie des nombres de Bordeaux

Ensembles normaux

Jacques Lesca, Michel Mendès France (1968/1969)

Séminaire de théorie des nombres de Bordeaux

Equidistribution in the dual group of the S -adic integers

Roman Urban (2014)

Czechoslovak Mathematical Journal

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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