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The central result of this chapter is Theorem 8.2, which completely describes measure-preserving (locally) 1-Lipschitz maps \(\mathbb {Z}_p^n{\twoheadrightarrow }\mathbb {Z}_p^m\) for \(m\leqslant n\) as well as ergodic (locally) 1-Lipschitz maps \(\mathbb {Z}_p^n{\twoheadrightarrow }\mathbb {Z}_p^n\) .

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The Main Ergodic Theorem for p-Adic 1-Lipschitz Maps

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  • 发表日期：

    2025年

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  • Vladimir Anashin

摘要

The central result of this chapter is Theorem 8.2, which completely describes measure-preserving (locally) 1-Lipschitz maps \(\mathbb {Z}_p^n{\twoheadrightarrow }\mathbb {Z}_p^m\) for \(m\leqslant n\) as well as ergodic (locally) 1-Lipschitz maps \(\mathbb {Z}_p^n{\twoheadrightarrow }\mathbb {Z}_p^n\) .