{"paper":{"title":"The Assouad dimensions of projections of planar sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.MG"],"primary_cat":"math.CA","authors_text":"Jonathan M. Fraser, Tuomas Orponen","submitted_at":"2015-09-03T15:38:03Z","abstract_excerpt":"We consider the Assouad dimensions of orthogonal projections of planar sets onto lines. Our investigation covers both general and self-similar sets.\n  For general sets, the main result is the following: if a set in the plane has Assouad dimension $s \\in [0,2]$, then the projections have Assouad dimension at least $\\min\\{1,s\\}$ almost surely. Compared to the famous analogue for Hausdorff dimension -- namely \\emph{Marstrand's Projection Theorem} -- a striking difference is that the words `at least' cannot be dispensed with: in fact, for many planar self-similar sets of dimension $s < 1$, we prov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01128","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"}