On the Dynamical Interpretation for the Quantum-Measurement Projection   Postulate
  An apparatus model with discrete momentum space suitable for the exact solution of the problem is considered. The special Hamiltonian of its interaction with the object system under consideration is chosen. In this simple case it is easy to illustrate how difficulties in constructing the dynamical interpretation of selective collapse could be overcomed without any limiting procedure. For this purpose one can apply either averaging with respect to a non-quantum parameter or reducing the algebra of the joint system operators (i. e. passing to the quantum system subalgebra). The latter procedure effectively implies averaging with respect to apparatus quantum variables not belonging to the system. 
R. L. Stratonovich and V. P. Belavkin