{
  "abstract": "Fix an integer $p\\geq 2$ and $0<s<1$. We construct an ergodic $\\times p$-invariant measure $μ$ on $\\mathbb T^2$ of dimension $s$, such that every line projection preserves dimension, including when the corresponding projected IFS has exact overlaps. In fact, our measure assigns mass $O(w^s)$ to every planar tube of width $w$. The result is sharp at the endpoint $s=1$ as shown by Pyörälä, Shmerkin, Suomala and Wu (2025). In contrast, we show that every quasi-Bernoulli $T_p$-invariant measure with positive dimension admits a dimension-dropping projection.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29569",
  "author_total": 1,
  "authors": [
    {
      "name": "Amir Algom"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ffby2zcytk7sf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29569",
  "fulltext_url": null,
  "id": "ffby2zcytk7sf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29569",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CA"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7204896999",
  "pdf_url": "https://arxiv.org/pdf/2608.29569",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ffby2zcytk7sf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.29569",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29569"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Ergodic $\\times p$-invariant measures on $\\mathbb{T}^2$ with no dimension dropping projections",
  "title_text": "Ergodic × p-invariant measures on 𝕋^2 with no dimension dropping projections",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/ffby2zcytk7sf",
  "venue": "arXiv",
  "versions": []
}