= Ahlswede–Daykin inequality
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= Four functions theorem
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For nonnegative functions on a finite <Boolean lattice>, the condition $\alpha(A)\beta(B)\le\gamma(A\cup B)\delta(A\cap B)$ for all pairs implies $(\sum\alpha)(\sum\beta)\le(\sum\gamma)(\sum\delta)$. Coordinate elimination and the <two-point four-functions inequality> prove it by induction. Indicators give inequalities for the <union and intersection of set families>. The Boolean-lattice statement appears in https://proceedings.neurips.cc/paper_files/paper/2012/file/03afdbd66e7929b125f8597834fa83a4-Paper.pdf[Theorem 3.1 of Nicholas Ruozzi's paper].
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