{"paper":{"title":"High density piecewise syndeticity of sumsets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.NT","authors_text":"Isaac Goldbring, Karl Mahlburg, Martino Lupini, Mauro Di Nasso, Renling Jin, Steven Leth","submitted_at":"2013-10-21T21:14:03Z","abstract_excerpt":"Renling Jin proved that if A and B are two subsets of the natural numbers with positive Banach density, then A+B is piecewise syndetic. In this paper, we prove that, under various assumptions on positive lower or upper densities of A and B, there is a high density set of witnesses to the piecewise syndeticity of A+B. Most of the result are shown to hold more generally for subsets of Z^d. The key technical tool is a Lebesgue density theorem for measure spaces induced by cuts in the nonstandard integers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5729","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"}