Variations On Terminology
The lattice condition for μ is also called multivariate total positivity, and sometimes the strong FKG condition; the term (multiplicative) FKG condition is also used in older literature.
The property of μ that increasing functions are positively correlated is also called having positive associations, or the weak FKG condition.
Thus, the FKG theorem can be rephrased as "the strong FKG condition implies the weak FKG condition".
Read more about this topic: FKG Inequality
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