Let's say I have made a measurement of some sort of a quantum system. That is, I have some macro/classical devices whose states have numbers associated with them, and their resulting states depend (in some way) on a quantum system. So I arrange the lab-plus-quantum system as desired and note down the numbers representing the states of the lab devices. How do I then infer that I have measured the momentum of something? I pose the question in terms of momentum rather than position because I suspect the position question may have a more straightforward answer. But I don't really know. As far as the theory is concerned, I can speak of the momentum operator, and write the down what should be the state of the system (given the initial conditions to be arranged in the lab) in terms of momentum eigenstates, etc. But how do I connect this with a particular actual measurement? I've read a few things over the years about quantum measurement theory but I have never seen a discussion of "Given an observable O, what conditions does the measuring apparatus have to satisfy for the result to be called a 'measurement of O'?" Anyone know any texts which cover this?