{
  "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}.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17516",
  "author_total": 3,
  "authors": [
    {
      "name": "Nishant Chandgotia"
    },
    {
      "name": "Zemer Kosloff"
    },
    {
      "name": "Shrey Sanadhya"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d0nyz2k5wk1n0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17516",
  "fulltext_url": null,
  "id": "d0nyz2k5wk1n0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17516",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7221778688",
  "pdf_url": "https://arxiv.org/pdf/2610.17516",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d0nyz2k5wk1n0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.17516",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17516"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Alpern Lemma Independent of a Partition for Aperiodic Systems",
  "title_text": "Alpern Lemma Independent of a Partition for Aperiodic Systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/d0nyz2k5wk1n0",
  "venue": "arXiv",
  "versions": []
}