  Long sequences of successive direct (projective) measurements or observations
of a few "uninteresting" physical quantities of a quantum system may reveal
indirect, but precise and unambiguous information on the values of some very
"interesting" observables of the system. In this paper, the mathematics
underlying this claim is developed; i.e., we attempt to contribute to a
mathematical theory of indirect and, in particular, non-demolition measurements
in quantum mechanics. Our attempt leads us to make novel uses of classical
notions and results of probability theory, such as the "algebra of functions
measurable at infinity", the Central Limit Theorem, results concerning relative
entropy and its role in the theory of large deviations, etc.
