  We show that, for the space of Borel probability measures on a Borel subset
of a Polish metric space, the extreme points of the Prokhorov,
Monge-Wasserstein and Kantorovich metric balls about a measure whose support
has at most n points, consist of measures whose supports have at most n+2
points. Moreover, we use the Strassen and Kantorovich-Rubinstein duality
theorems to develop representations of supersets of the extreme points based on
linear programming, and then develop these representations towards the goal of
their efficient computation.
