An inequality on paths in a grid
Journal of Combinatorial Theory Series A
A generalization of the Ahlswede-Daykin inequality
Discrete Mathematics
Inequalities for cross-unions of collections of finite sets
European Journal of Combinatorics
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We prove the following theorem, which is an analog for discrete set functions of a geometric result of Lovász and Simonovits. Given two real-valued set functions f1, f2 defined on the subsets of a finite set S satisfying, ΣX⊆S fi(X) ≥0 for i ∈ {1, 2}, there exists a positive multiplicative set function µ over S and two subsets A, B ⊆ S such that for i ∈ {1,2} µ(A)fi(A)+µ(B)fi(B)+µ(A∪B)fi(A∪ B) + µ(A ∩ B)fi (A∩B) ≥0. The Ahlswede-Daykin four function theorem can be deduced easily from this.