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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","authors_text":"Carlos Gustavo Moreira, Jorge Erick L\\'opez","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-07-03T02:46:47Z","title":"A generalization of Marstrand's theorem for projections of cartesian products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0424","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a101531e74d67f822fc69e41c4febd4397feaef65196281cf6d2f16e76f14ba2","target":"record","created_at":"2026-05-18T04:18:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"7a462d740dd4d9f449984dadc9f190f13b242842f97c7cf1198a1cdfac5751b1","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-07-03T02:46:47Z","title_canon_sha256":"54b2abc65bfc2f2c30d84358a4d99e0c9b235d0be27e77a3acfa373c879d9e32"},"schema_version":"1.0","source":{"id":"1107.0424","kind":"arxiv","version":1}},"canonical_sha256":"fa6016bae3025a11d86d9f4fa008921b0106f0d2b1f77ffabac02afb62e36cf2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa6016bae3025a11d86d9f4fa008921b0106f0d2b1f77ffabac02afb62e36cf2","first_computed_at":"2026-05-18T04:18:53.998651Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:53.998651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eJdTotHMguo1Xm8KppPRz96Kglam/BB29X6RaV+X1cjZqh592RyFxevl5s+x3NW6MSHJK8KQREPCvOkWk7t2Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:53.999117Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.0424","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a101531e74d67f822fc69e41c4febd4397feaef65196281cf6d2f16e76f14ba2","sha256:4b45d69c098a07c8a6a5ad2c75672ed81c74623508e6b69ace2b484078bfb85e"],"state_sha256":"41c0cea182f099aace47d1ec74ec4b4520795cbe337d46e10419c2448d8ee545"}