Ahlswede-Daykin inequality

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four-functions inequality

An inequality in which an inequality for four functions on a finite distributive lattice applies also to additive extensions of the functions on lattice subsets. Let be a finite distributive lattice (see also FKG inequality), such as the power set of a finite set ordered by proper inclusion. For subsets , of , define and . If or is empty, . Given , let .

The Ahlswede–Daykin inequality says that if , , , and map into such that


See [a1] or [a2], [a4], [a7] for a proof.

The inequality is very basic and is used in proofs of other inequalities (cf. [a2], [a3], [a4], [a5], [a7]), including the FKG inequality [a6] and the Fishburn–Shepp inequality [a3], [a8].

See also Correlation inequalities; Holley inequality.


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Ahlswede–Daykin inequality. Encyclopedia of Mathematics. URL: