  We previously remarked that when an observable A has a continuous spectrum,
then von Neumann's formula for the post-measurement state needs to be extended
and the correct formula ineluctably involves the resolution of the detector
used in the measurement. We generalize previous results to compute the
uncertainties in successive measurements of more general pairs of observables.
We also show that this extended von Neumann's formula for the post-measurement
state is a completely positive map and, moreover, that there is a
completely-positive interpolation between the pre- and post-measurement states.
Weinberg has advocated that the time-evolution during the measurement process
should be modeled as an open quantum system and governed by a Lindblad
equation. We verify that this is indeed the case for an arbitrary observable,
A, and a fairly general class of interpolations.
