Koszul configurations of points in projective spaces

We prove a new criterion for the homogeneous coordinate ring of a finite set of points in ${\Bbb P}^n$ to be Koszul. Like the well known criterion due to Kempf it involves only incidence conditions on linear spans of subsets of a given set. We also give a sufficient condition for the Koszul property to be preserved when passing to a subset of a finite set of points in ${\Bbb P}^n$.