The following two claims have been put forward in support of an indivi
dual interpretation of quantum mechanics: within the framework of quan
tum measurement theory, (i) the concept of measurement of a sharp obse
rvable can be completely characterized in terms of the notion of calib
ration, and (ii) the frequency interpretation of probability (of a mea
surement outcome) can be founded on the notion of a property of an ind
ividual system. Here we set out to generalize these results to measure
ment schemes which may be unitary or non-unitary and to object and poi
nter observables which may be sharp or unsharp.