Sibley and Sempi have constructed metrics on the space of probability distribution functions with the property that weak convergence of a sequence is equivalent to metric convergence. Sibley's work is a modification of Levy's metric, but Sempi's construction is of a different sort. Here we construct a family of metrics having the same convergence properties as Sibley's and Sempi's but which does not appear to be related to theirs in any simple way. Some instances are brought out in which the metrics have probabilistic interpretations.
@article{urn:eudml:doc:38925,
title = {New metrics for weak convergence of distribution functions.},
journal = {Stochastica},
volume = {9},
year = {1985},
pages = {5-17},
zbl = {0607.60004},
mrnumber = {MR0823225},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:38925}
}
Taylor, Michael D. New metrics for weak convergence of distribution functions.. Stochastica, Tome 9 (1985) pp. 5-17. http://gdmltest.u-ga.fr/item/urn:eudml:doc:38925/