  We analyze in mathematical detail, within the framework of the QMUPL model of
spontaneous wave function collapse, the von Neumann measurement scheme for the
measurement of a 1/2 spin particle. We prove that, according to the equation of
the model: i) throughout the whole measurement process, the pointer of the
measuring device is always perfectly well localized in space; ii) the
probabilities for the possible outcomes are distributed in agreement with the
Born probability rule; iii) at the end of the measurement the state of the
microscopic system has collapsed to the eigenstate corresponding to the
measured eigenvalue. This analysis shows rigorously how dynamical reduction
models provide a consistent solution to the measurement problem of quantum
mechanics.
