  We study the positive-operator-valued measures on the projective real line
covariant with respect to the projective group, assuming that the energy is a
positive operator. This problem is similar to the more complicated problem of
finding the positive-operator-valued measures on the compactified Minkowski
space-time covariant with respect to the conformal group. It also describes a
time-of-arrival observable for a free particle covariant with respect to linear
canonical transformations.
