Solution
= Solution
Each factor $f_{j\mid\operatorname{pa}(j)}$ depends only on node $j$ and its parents. Those vertices form a clique in the <moral graph>, because moralization joins every pair of parents and removes arrow directions. The positive joint density therefore factors into clique potentials of the moral graph. The <Hammersley-Clifford theorem> then implies the global Markov property for that undirected graph.