Let $G=(V,E)$ be a finite simple graph, and let $\{X_i\}_{i \in V}$ be a collection of random variables associated with the vertices of $G$. The joint distributions of these r.v.s is a *Markov Random Field* if, for any three subsets $U,W,C \subset V$ such that $C$ separates $U$ from $W$ (i.e., any path from $U$ to $W$ passes through $C$), it holds that conditioned on the r.v.s in $C$, the r.v.s in $U$ are independent from those in $W$. This is called the *global Markov property*. An implication is the *pairwise Markov property*, which states that for all $(i,j) \not \in E$, $X_i$ is independent of $X_j$, conditioned on the rest of the r.v.s.

A finite distribution over $\{X_i\}$ is called *positive* if every combination of assignments has positive probability (here "every" means those whose marginals are positive). I am looking for a reference for the fact that for positive distributions, the pairwise Markov property implies the global Markov property. Thanks!