The space of distribution functions endowed with the metric introduced in [5] is separable.
@article{urn:eudml:doc:38881, title = {The space of distribution functions is separable.}, journal = {Stochastica}, volume = {7}, year = {1983}, pages = {197-200}, zbl = {0557.60015}, mrnumber = {MR0773823}, language = {en}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:38881} }
Sempi, Carlo. The space of distribution functions is separable.. Stochastica, Tome 7 (1983) pp. 197-200. http://gdmltest.u-ga.fr/item/urn:eudml:doc:38881/