{"paper":{"title":"On Sums of Nearly Affine Cantor Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DS","authors_text":"Anton Gorodetski, Scott Northrup","submitted_at":"2015-10-23T18:30:49Z","abstract_excerpt":"For a compact set $K\\subset \\mathbb{R}^1$ and a family $\\{C_\\lambda\\}_{\\lambda\\in J}$ of dynamically defined Cantor sets sufficiently close to affine with $\\text{dim}_H\\, K+\\text{dim}_H\\, C_\\lambda>1$ for all $\\lambda\\in J$, under natural technical conditions we prove that the sum $K+C_\\lambda$ has positive Lebesgue measure for almost all values of the parameter $\\lambda$. As a corollary, we show that generically the sum of two affine Cantor sets has positive Lebesgue measure provided the sum of their Hausdorff dimensions is greater than one."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.07008","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"}