Alpern Lemma Independent of a Partition for Aperiodic Systems

Nishant Chandgotia; Zemer Kosloff; Shrey Sanadhya

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arXiv · 2610.17516

Alpern Lemma Independent of a Partition for Aperiodic Systems

Nishant Chandgotia·Zemer Kosloff·Shrey Sanadhya

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Abstract

We prove that for every $(X,\mathcal{B},μ,T)$, an aperiodic, probability preserving system and $\mathcal{P}$ a finite measurable partition of $X$, there exists an Alpern Multitower whose base is independent of $\mathcal{P}$. This removes the ergodicity assumption in the original proof of the independent Alpern Lemma of \cite{MR3373823}. As a consequence, we remove ergodicity assumption from recent results on limit theorems in deterministic systems \cite{Kosloff_Volny_2022,kosloffVolnyStableCLT,MR4955410}.

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BibTeX RIS

Nishant Chandgotia, Zemer Kosloff, Shrey Sanadhya. 2026-10-13. Alpern Lemma Independent of a Partition for Aperiodic Systems. https://arxiv.org/abs/2610.17516

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