{"paper":{"title":"Constancy results for special families of projections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Katrin F\\\"assler, Tuomas Orponen","submitted_at":"2012-08-09T11:19:00Z","abstract_excerpt":"Let {\\mathbb{V} = V x R^l : V \\in G(n-l,m-l)} be the family of m-dimensional subspaces of R^n containing {0} x R^l, and let \\pi_{\\mathbb{V}} : R^n --> \\mathbb{V} be the orthogonal projection onto \\mathbb{V}. We prove that the mapping V \\mapsto Dim \\pi_{\\mathbb{V}}(B) is almost surely constant for any analytic set B \\subset R^n, where Dim denotes either Hausdorff or packing dimension."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1876","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":""},"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"}