Traditionally, in quantum mechanics a measurement "breaks the system": the state of the system is instantaneously modified in a way that does not follow the normal equation of motion (the Schrödinger equation). This is known as the "collapse of the wave function". The paper shows that there is a way in principle to include the measurement apparatus also within the quantum description, in such a way that the interaction with the system causes the system to eventually evolve into a state that corresponds exactly to the one that results from the traditional collapse of the wave function (but without a "break" in the description). It therefore supports the idea that classical behavior is an emergent phenomenon from the underlying quantum behavior, and that there is no fundamental classical-quantum divide