{
  "abstract": "Let $\\mathcal{N}^h_Ω$ be the null ideal of the Hausdorff measure constructed by Davies and Rogers. We give a Tukey reduction of $(\\mathcal{N}^h_Ω,\\mathcal{N}^h_Ω,\\subseteq)$ to a localization system with finite coordinate sets. It follows that $\\mathfrak{v}^\\forall_{D,g}\\le\\operatorname{add}(\\mathcal{N}^h_Ω)$ and $\\operatorname{cof}(\\mathcal{N}^h_Ω)\\le\\mathfrak{c}^\\forall_{D,g}$ for some $D, g \\in ω^ω$. Consequently, we prove the consistency of $\\mathfrak{d}<\\operatorname{add}(\\mathcal{N}^h_Ω)$ and, separately, $\\operatorname{cof}(\\mathcal{N}^h_Ω)<\\mathfrak{b}$. Hence the additivity and cofinality of $\\mathcal{N}^h_Ω$ can differ from those of the Lebesgue null ideal. We also show that the finite graphs in the Davies--Rogers construction can be chosen so that $\\operatorname{cov}(\\mathcal{N}^h_Ω)\\le\\operatorname{non}(\\mathcal{N}^h_Ω)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08549",
  "author_total": 1,
  "authors": [
    {
      "name": "Tatsuya Goto"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c0v9g8mqbfazq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08549",
  "fulltext_url": null,
  "id": "c0v9g8mqbfazq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08549",
  "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.LO"
    ],
    [
      "openalex",
      "2608|Advanced Topology and Set Theory"
    ]
  ],
  "openalex": "W7220953777",
  "pdf_url": "https://arxiv.org/pdf/2610.08549",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c0v9g8mqbfazq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.08549",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08549"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "The additivity of a certain Hausdorff measure can differ from that of the Lebesgue measure",
  "title_text": "The additivity of a certain Hausdorff measure can differ from that of the Lebesgue measure",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/c0v9g8mqbfazq",
  "venue": "arXiv",
  "versions": []
}