  Most metrics between finite point measures currently used in the literature
have the flaw that they do not treat differing total masses in an adequate
manner for applications. This paper introduces a new metric $\bar{d}_1$ that
combines positional differences of points under a closest match with the
relative difference in total mass in a way that fixes this flaw. A
comprehensive collection of theoretical results about $\bar{d}_1$ and its
induced Wasserstein metric $\bar{d}_2$ for point process distributions are
given, including examples of useful $\bar{d}_1$-Lipschitz continuous functions,
$\bar{d}_2$ upper bounds for Poisson process approximation, and $\bar{d}_2$
upper and lower bounds between distributions of point processes of i.i.d.
points. Furthermore, we present a statistical test for multiple point pattern
data that demonstrates the potential of $\bar{d}_1$ in applications.
