{
  "abstract": "We prove sharp bounds for the upper and lower intermediate dimensions of orthogonal and radial projections of compactly supported measures. Both dimension functions are preserved almost everywhere when the quasi-Assouad dimension does not exceed the target dimension. We obtain exceptional-set estimates using the entire source dimension function, with sharpness for explicit families. We also construct a fixed measure whose projected dimension functions vary on open direction sets, even when all source dimensions lie below the target dimension.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32808",
  "author_total": 4,
  "authors": [
    {
      "name": "Shengyang Zang"
    },
    {
      "name": "Yingyu Zhao"
    },
    {
      "name": "Yunhao Zhao"
    },
    {
      "name": "Chen Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6rty5q3q6zaf9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32808",
  "fulltext_url": null,
  "id": "6rty5q3q6zaf9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32808",
  "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"
    ],
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      "openalex",
      "2610|Mathematical Dynamics and Fractals"
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  "openalex": "W7223651238",
  "pdf_url": "https://arxiv.org/pdf/2610.32808",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6rty5q3q6zaf9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.32808",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32808"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Sharp Projection Bounds for Intermediate Dimensions of Measures",
  "title_text": "Sharp Projection Bounds for Intermediate Dimensions of Measures",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/6rty5q3q6zaf9",
  "venue": "arXiv",
  "versions": []
}