{"paper":{"title":"Random constructions for translates of non-negative functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CA","authors_text":"Bal\\'azs Maga, Bruce Hanson, G\\'asp\\'ar V\\'ertesy, Zolt\\'an Buczolich","submitted_at":"2018-04-27T09:17:54Z","abstract_excerpt":"Suppose $\\Lambda$ is a discrete infinite set of nonnegative real numbers. We say that $ {\\Lambda}$ is type $2$ if the series $s(x)=\\sum_{\\lambda\\in\\Lambda}f(x+\\lambda)$ does not satisfy a zero-one law. This means that we can find a non-negative measurable \"witness function\"\n  $f: {\\mathbb R}\\to [0,+ {\\infty})$ such that both the convergence set $C(f, {\\Lambda})=\\{x: s(x)<+ {\\infty} \\}$ and its complement the divergence set $D(f, {\\Lambda})=\\{x: s(x)=+ {\\infty} \\}$ are of positive Lebesgue measure. If $ {\\Lambda}$ is not type $2$ we say that $ {\\Lambda}$ is type $1$.\n  The main result of our pa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.10408","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"}