A characterization of functions with vanishing averages over products of disjoint sets
نویسندگان
چکیده
Given α1, . . . , αm ∈ (0, 1), we characterize all integrable functions f : [0, 1] → C satisfying ∫ A1×···×Am f = 0 for any collection of disjoint measurable sets A1, . . . , Am ⊆ [0, 1] of respective measures α1, . . . , αm. We use this characterization to settle some of the conjectures in [S. Janson and V. Sós, More on quasi-random graphs, subgraph counts and graph limits, European J. Combin. 46 (2015), 134–160] about the relation between subgraph counts and quasi-randomness. AMS Subject Classification: 05C80
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ورودعنوان ژورنال:
- Eur. J. Comb.
دوره 56 شماره
صفحات -
تاریخ انتشار 2016