{"paper":{"title":"A Marstrand-type restricted projection theorem in $\\mathbb{R}^{3}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CA","authors_text":"Antti K\\\"aenm\\\"aki, Laura Venieri, Tuomas Orponen","submitted_at":"2017-08-16T12:38:48Z","abstract_excerpt":"Marstrand's projection theorem from $1954$ states that if $K \\subset \\mathbb{R}^{3}$ is an analytic set, then, for $\\mathcal{H}^{2}$ almost every $e \\in S^{2}$, the orthogonal projection $\\pi_{e}(K)$ of $K$ to the line spanned by $e$ has Hausdorff dimension $\\min\\{\\dim_{\\mathrm{H}} K,1\\}$. This paper contains the following sharper version of Marstrand's theorem. Let $V \\subset \\mathbb{R}^{3}$ be any $2$-plane, which is not a subspace. Then, for $\\mathcal{H}^{1}$ almost every $e \\in S^{2} \\cap V$, the projection $\\pi_{e}(K)$ has Hausdorff dimension $\\min\\{\\dim_{\\mathrm{H}} K,1\\}$. For $0 \\leq t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04859","kind":"arxiv","version":2},"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/1708.04859/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"}