  The quantum measurement problem is formulated in the form of an insolubility
theorem that states the impossibility of obtaining, for all available object
preparations, a mixture of states of the compound object and apparatus system
that would represent definite pointer positions. A proof is given that
comprises arbitrary object observables, whether sharp or unsharp, and besides
sharp pointer observables a certain class of unsharp pointers, namely, those
allowing for the property of pointer value definiteness. A recent result of H.
Stein is applied to allow for the possibility that a given measurement may not
be applicable to all possible object states but only to a subset of them. The
question is raised whether the statement of the insolubility theorem remains
true for genuinely unsharp observables. This gives rise to a precise notion of
unsharp objectification.
