{"paper":{"title":"Slicing Sets and Measures, and the Dimension of Exceptional Parameters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Tuomas Orponen","submitted_at":"2010-10-27T11:23:11Z","abstract_excerpt":"We consider the problem of slicing a compact metric space \\Omega with sets of the form \\pi_{\\lambda}^{-1}\\{t\\}, where the mappings \\pi_{\\lambda} \\colon \\Omega \\to \\R, \\lambda \\in \\R, are \\emph{generalized projections}, introduced by Yuval Peres and Wilhelm Schlag in 2000. The basic question is: assuming that \\Omega has Hausdorff dimension strictly greater than one, what is the dimension of the 'typical' slice \\pi_{\\lambda}^{-1}{t}, as the parameters \\lambda and t vary. In the special case of the mappings \\pi_{\\lambda} being orthogonal projections restricted to a compact set \\Omega \\subset \\R^{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5647","kind":"arxiv","version":3},"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"}