And if p is a Markov network on G, then I_{sep}(G)\subset I(p) as you wrote. ]]>

We've seen this definition: (1)

\begin{align} I_{sep}(G) = \{X \perp Y | Z : Z \ separates \ X \ and \ Y\} \end{align}

Does this definition rely on some probability? Or is it that given a graph G we construct the set of **all** X,Y,Z where Z separates X and Y and then, given a probability p we say that:

\begin{align} I_{sep}(G) \subseteq I(p) \end{align}

If p satisfies all these properties?

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