{"paper":{"title":"A generalization of Marstrand's theorem for projections of cartesian products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CA","authors_text":"Carlos Gustavo Moreira, Jorge Erick L\\'opez","submitted_at":"2011-07-03T02:46:47Z","abstract_excerpt":"We prove the following variant of Marstrand's theorem about projections of cartesian products of sets:\n  Let $K_1,...,K_n$ Borel subsets of $\\mathbb R^{m_1},... ,\\mathbb R^{m_n}$ respectively, and $\\pi:\\mathbb R^{m_1}\\times...\\times\\mathbb R^{m_n}\\to\\mathbb R^k$ be a surjective linear map. We set $$\\mathfrak{m}:=\\min\\{\\sum_{i\\in I}\\dim_H(K_i) + \\dim\\pi(\\bigoplus_{i\\in I^c}\\mathbb R^{m_i}), I\\subset\\{1,...,n\\}, I\\ne\\emptyset\\}.$$ Consider the space $\\Lambda_m=\\{(t,O), t\\in\\mathbb R, O\\in SO(m)\\}$ with the natural measure and set $\\Lambda=\\Lambda_{m_1}\\times...\\times\\Lambda_{m_n}$. For every $\\l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0424","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"}