{"paper":{"title":"A characterization of functions with vanishing averages over products of disjoint sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Hamed Hatami, Pooya Hatami, Yaqiao Li","submitted_at":"2014-11-10T02:45:00Z","abstract_excerpt":"Given $\\alpha_1,...,\\alpha_m \\in (0,1)$, we characterize all integrable functions $f:[0,1]^m \\to \\mathbb{C}$ satisfying $\\int_{A_1 \\times ...\\times A_m} f =0$ for any collection of disjoint sets $A_1,...,A_m \\subseteq [0,1]$ of respective measures $\\alpha_1,...,\\alpha_m$. We use this characterization to settle some of the conjectures in [S. Janson and V. S\\'os, More on quasi-random graphs, subgraph counts and graph limits, arXiv:1405.6808]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2314","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"}