Sahi's generalized FKG conjecture for multilinear functionals

Let $L$ be a distributive lattice equipped with a probability measure $mu$ satisfying

$$\mu(a\vee b)\mu(a\wedge b)\geq\mu(a)\mu(b)$$

for all $a,b\in L$; such an $L$ is an FKG poset. Let $f_1,\ldots,f_n$ be positive monotone decreasing functions on $L$, and let $E_n(f_1,\ldots,f_n)$ denote Sahi's multilinear functionals extending expectation and correlation. Sahi's generalized FKG conjecture. For every $n\geq 1$,

$$E_n(f_1,\ldots,f_n)\geq 0.$$

This conjecture extends the FKG inequality from two functions to arbitrarily many positive monotone functions and is intended to provide a useful generalized correlation inequality in probability, combinatorics, statistics, and physics. Its resolution is not given in the source.