  Properties of sharp observables (normalized PV measures) in relation to
smearing by a Markov kernel are studied. It is shown that for a sharp
observable $P$ defined on a standard Borel space, and an arbitrary observable
$M$, the following properties are equivalent: (a) the range of $P$ is contained
in the range of $M$; (b) $P$ is a function of $M$; (c) $P$ is a smearing of
$M$.
