Several Remarks on Pascal Automorphismand Infinite Ergodic Theory

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Submitted: 2024-12-18; Published: 2024-12-18

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Abstract

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.