Markov chain [mathematical expression not reproducible] takes values in a
countably infinite set D with transition probability matrix P = [p(i,j)], where p(i, j) = P([s.sub.t+1] = j | [s.sub.t] = i), and P is nondegenerate, P([s.sub.0] = i) > 0 for all i [member of] D.
Let x = {[x.sub.i], [x.sub.2], ...} be a
countably infinite set of variables.
40, a set X being infinite, it can be expressed as a disjoint union of a class C of
countably infinite sets that is, each of which has cardinality [omega].