{"paper":{"title":"Measures supported on partly normal numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CA","authors_text":"Junqiang Zhang, Malabika Pramanik","submitted_at":"2024-08-06T23:10:38Z","abstract_excerpt":"A real number $x$ is normal with respect to an integer base $b \\geq 2$ if its digit expansion in this base is ``equitable'', in the sense that for $k \\geq 1$, every ordered sequence of $k$ digits from $\\{0, 1, \\ldots, b-1\\}$ occurs in the digit expansion of $x$ with the same limiting frequency. Borel's classical result \\cite{b09} asserts that Lebesgue-almost every number $x$ is normal in every base $b \\geq 2$. This three-part article considers sets of partial normality. Given any choice of integer bases $\\mathscr{B}, \\mathscr{B}' \\subseteq \\{2, 3, \\ldots\\}$, we investigate measure-theoretic pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.03473","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2408.03473/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}