Several Remarks on Pascal Automorphismand Infinite Ergodic Theory

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Several Remarks on Pascal Automorphismand Infinite Ergodic Theory Anatoly Vershik

We interpret the Pascal-adic transformation asa generalized induced automorphism (over odometer) and for-mulate theσ-finite analog of odometer which is also known as”Hajian-Kakutani transformation” (former ”Ohio state exam-ple”). We shortly suggest a sketch of the theory of random walkson the groups on the base ofσ-finite ergodic theory.

DOI: https://armjmath.sci.am/index.php/ajm/article/view/114 Armenian Journal of Mathematics, 7(2) 85-96

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Keywords

infinite measure space, ergodic, measure preserving transforma-tion, random walk, adic transformation, Pascal automorphism, odometer.

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