  The postulates of von Neumann and L\"uders concerning measurements in quantum
mechanics are discussed and criticized in the context of a simple model
proposed by Gisin. The main purpose of our paper is to analyze some
mathematical aspects of that model and to draw some general lessons on the
so-called ``measurement problem'' in quantum mechanics pointing towards the
need to introduce general principles that determine the law for the stochastic
time evolution of states of individual physical systems.
