Holley inequality

An inequality for a finite distributive lattice , saying that if and map into and satisfy and

then

for every that is non-decreasing in the sense that implies . It is due to R. Holley [a4] and was motivated by the related FKG inequality [a3]. It is an easy corollary [a2] of the more powerful Ahlswede–Daykin inequality [a1].

See also Correlation inequalities; Fishburn–Shepp inequality.

References

[a1]	R. Ahlswede, D.E. Daykin, "An inequality for the weights of two families, their unions and intersections" Z. Wahrscheinlichkeitsth. verw. Gebiete , 43 (1978) pp. 183–185
[a2]	P.C. Fishburn, "Correlation in partially ordered sets" Discrete Appl. Math. , 39 (1992) pp. 173–191
[a3]	C.M. Fortuin, P.N. Kasteleyn, J. Ginibre, "Correlation inequalities for some partially ordered sets" Comm. Math. Phys. , 22 (1971) pp. 89–103
[a4]	R. Holley, "Remarks on the FKG inequalities" Comm. Math. Phys. , 36 (1974) pp. 227–231