  The measurability by means of continuous measurements, of an observable
$\A(t_0)$, at an instant, and of a time averaged observable, $\bar \A=1/T\int
\A(t')dt'$, is examined for linear and in particular for non-linear quantum
mechanical systems. We argue that only when the exact (non-perturbative)
solution is known, an exact measurement may be possible. A perturbative
approach is shown to fail in the non-linear case for measurements with accuracy
$\Delta \bar \A < \Delta \bar \A_{min}(T)$, giving rise to a restriction on the
accuracy. Thus, in order to prepare an initial pure state of a non-linear
system, by means of a continuous measurement, the exact non-perturbative
solution must be known.
