First encounter with the term, I'd like some help understanding it. I know there are several approaches, but this one is important to me because I'm trying to understand an article that uses it throughout its text. Definition: Let G=(V,E) be a finite (connected) graph and let S be a finite set. A random element X taking values in [tex]S^V[/tex] is said to be a Markov random field if for each [tex]W\subset V[/tex], the conditional distribution of X(W) given X(V\W) depends on X(V\W) only through its values on [tex]\partial W[/tex]. It goes on to write this mathematically, which I will write down here if you ask me to. My problem is with the phrase "A random element X taking values in...". I just want to know from where to where X is. Obviously X takes values in [tex]S^V[/tex], so this is the range of X. What is its domain?