PreprintCC BY 4.0arXiv
Alpern Lemma Independent of a Partition for Aperiodic Systems
Abstract
We prove that for every (X,ℬ,μ,T), an aperiodic, probability preserving system and 𝒫 a finite measurable partition of X, there exists an Alpern Multitower whose base is independent of 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
@misc{chandgotia2026alpern,
title = {{Alpern Lemma Independent of a Partition for Aperiodic Systems}},
author = {Nishant Chandgotia and Zemer Kosloff and Shrey Sanadhya},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17516},
eprint = {2610.17516},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17516},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Alpern Lemma Independent of a Partition for Aperiodic Systems
AU - Nishant Chandgotia
AU - Zemer Kosloff
AU - Shrey Sanadhya
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.17516
UR - https://arxiv.org/abs/2610.17516
AB - We prove that for every (X,ℬ,μ,T), an aperiodic, probability preserving system and 𝒫 a finite measurable partition of X, there exists an Alpern Multitower whose base is independent of 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}.
ER -