The Prokhorov metric compares probability measures on a metric space by allowing both a small enlargement
of sets and a small error in mass. For measures 
, it is
 |
where 
is the set of points at distance
less than 
from 
. On a separable metric space it metrizes weak
convergence of probability measures. Combined
with Hausdorff distance in a common ambient
space, it gives the Gromov-Hausdorff-Prokhorov
distance used for random planar map limits.
