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.
