A characterization of functions with vanishing averages over products of disjoint sets. (August 2016) - Hatami, Hamed; Hatami, Pooya; Li, Yaqiao
Abstract: Given α 1, …, α m ∈ ( 0, 1 ), we characterize all integrable functions f : [ 0, 1 ] m → C satisfying ∫ A 1 × ⋯ × A m f = 0 for any collection of disjoint measurable sets A 1, …, A m ⊆ [ 0, 1 ] of respective measures α 1, …, α m . We use this characterization to settle some of the conjectures in Janson and Sós (2015) about the relation between subgraph counts and quasi-randomness.