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arXiv · 2608.20004

Sets of nice recurrence are partition regular

Jonathan Chapman
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Abstract

A set of positive integers $R$ is called a set of nice recurrence if for any measure preserving system $(X,\mu,T)$, for all measurable $A\subseteq X$, and each $\varepsilon>0$, there exists $n\in R$ such that $\mu(A\cap T^{-n}A)\geqslant \mu(A)^2 - \varepsilon$. Answering a long-standing question of Bergelson, we show that sets of nice recurrence have the following Ramsey property: any finite colouring of a set of nice recurrence admits a monochromatic set of nice recurrence.

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Jonathan Chapman. 2026-08-20. Sets of nice recurrence are partition regular. https://arxiv.org/abs/2608.20004

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