{"paper":{"title":"On the absolute continuity of radial and linear projections of missing digits measures","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.MG","authors_text":"Han Yu","submitted_at":"2023-09-04T00:40:13Z","abstract_excerpt":"In this paper, we study the absolute continuity of radial projections of missing digits measures. We show that for large enough missing digits measures $\\lambda$ on $\\mathbb{R}^n,n\\geq 2,$ for all $x\\in\\mathbb{R}^n\\setminus \\mathrm{supp}(\\lambda),$ $\\Pi_x(\\lambda)$ is absolutely continuous with a density function in $L^2(S^{n-1}).$ Our method applies to linear projections as well. In particular, we show that for $\\lambda$ as above, the linearly projected measure $P_\\theta(\\lambda)$ is absolutely continuous with a continuous density function for almost all directions $\\theta\\in S^{n-1}.$ This i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.01298","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/2309.01298/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"}