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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the Lévy-Prokhorov metric (sometimes known just as the Prokhorov metric) is a metric (i.e., a definition of distance) on the collection of probability measures on a given metric space. It is named after the French mathematician Paul Pierre Lévy and the Soviet mathematician Yuri Vasilevich Prokhorov; Prokhorov introduced it in 1956 as a generalization of the earlier Lévy metric.Some authors omit one of the two inequalities or choose only open or closed A; either inequality implies the other, but restricting to open/closed sets changes the metric so defined.