We introduce the topology of convergence in distribution of masses on the real line and state its pseudometrizability, by introducing two equivalent pseudometrics (suitable modifications of the Lévy metric and Kingman-Taylor metric, both considered, in the Literature, in the context of σ-additive probability distribution functions). Moreover, we prove that any bounded set of masses is relatively compact w.r.t. this topology. Finally, we show that the corresponding topological space is a locally compact Polish space.
