Theoretical Probability and Random Processes.
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13. A function d: S × S → R is called a metric on S if: (i) d(s, t) = d(t, s) ≥ 0 for all s, t = S, (ii) d (s, t) = 0 if and only if s = =t, and (iii) d(s, t) ≤ d(s, u) + d(u, t) for all s, t,