{
  "abstract": "On a metric space equipped with a doubling measure supporting a Poincaré inequality, we introduce capacity-relaxed infinitesimal Lipschitz numbers and characterize Newtonian functions in $N^{1,p}$, $1\\le p\\le\\infty$, and functions of bounded variation. If $X$ is additionally $Q$-regular, then every BV function is $1$-finely differentiable at $μ$-almost every point, and its fine differential agrees with its approximate Cheeger differential. We also extend a Sobolev regularity criterion from continuous to $p$-quasicontinuous functions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29359",
  "author_total": 2,
  "authors": [
    {
      "name": "Panu Lahti"
    },
    {
      "name": "Yuxin Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/62n369a750sqm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29359",
  "fulltext_url": null,
  "id": "62n369a750sqm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29359",
  "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.MG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7223226022",
  "pdf_url": "https://arxiv.org/pdf/2610.29359",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/62n369a750sqm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.29359",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29359"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Lipschitz numbers and fine differentiability on metric measure spaces",
  "title_text": "Lipschitz numbers and fine differentiability on metric measure spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/62n369a750sqm",
  "venue": "arXiv",
  "versions": []
}