Show that the Lvy metric of Durrett Exercise 3.2.6 makes the space of probability measures on the line into a complete separable metric space. 3.2.6. The Lvy Metric. Show that p(F, G) = inf{e : F(:.v: e) E S SCH) g F(a: + e) + e for all :3} denes a. metric on the space of distributions and p(Fm F) > 0 if and only if F1.1 => F