  In this paper, we present a collection of results on the observability of
quantum mechanical systems, in the case the output is the result of a discrete
nonselective measurement. By defining an effective observable we extend
previous results, on the Lie algebraic characterization of observable systems,
to general measurements. Further results include the characterization of a
`best probe' (i.e. a minimally disturbing probe) in indirect measurement and a
study of the relation between disturbance and observability in this case. We
also discuss how the observability properties of a quantum system relate to the
problem of state reconstruction. Extensions of the formalism to the case of
selective measurements are also given.
