On measure-preserving $\mathbb{F}_{p}^{\omega}$-systems of order k

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2025年7月13日

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Pablo Candela,
Diego González-Sánchez,
Balázs Szegedy

摘要

Building on previous work in the nilspace-theoretic approach to the study of Host–Kra factors of measure-preserving systems, we prove that every ergodic $\mathbb{F}_{p}^{\omega}$ $F_{p}^{ω}$ -system of order k is a factor of an Abramov $\mathbb{F}_{p}^{\omega}$ $F_{p}^{ω}$ -system of order k. This answers a question of Jamneshan, Shalom and Tao.

On measure-preserving \(\mathbb{F}_{p}^{\omega}\)-systems of order k

摘要