{"paper":{"title":"On the absolute continuity of radial projections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CA","authors_text":"Tuomas Orponen","submitted_at":"2017-09-14T08:02:26Z","abstract_excerpt":"Let $d \\geq 2$ and $d - 1 < s < d$. Let $\\mu$ be a compactly supported Radon measure in $\\mathbb{R}^{d}$ with finite $s$-energy. I prove that the radial projections $\\pi_{x\\sharp}\\mu$ of $\\mu$ are absolutely continuous with respect to $\\mathcal{H}^{d - 1}$ for every centre $x \\in \\mathbb{R}^{d} \\setminus \\operatorname{spt} \\mu$, outside an exceptional set of dimension at most $2(d - 1) - s$. This is sharp. In fact, for $x$ outside an exceptional set as above, $\\pi_{x\\sharp}\\mu \\in L^{p}(S^{d - 1})$ for some $p > 1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04653","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":""},"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"}