The topology of convergence in distribution of masses on the real line

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.