  We treat the events determined by a quantum physical state in a
noncommutative space-time, generalizing the analogous treatment in the usual
Minkowski space-time based on positive-operator-valued measures (POVMs). We
consider in detail the model proposed by Snyder in 1947 and calculate the POVMs
defined on the real line that describe the measurement of a single coordinate.
The approximate joint measurement of all the four space-time coordinates is
described in terms of a generalized Wigner function (GWF). We derive lower
bounds for the dispersion of the coordinate observables and discuss the
covariance of the model under the Poincare' group. The unusual transformation
law of the coordinates under space-time translations is interpreted as a
failure of the absolute character of the concept of space-time coincidence. The
model shows that a minimal length is compatible with Lorents covariance.
