  We derive a master equation describing the evolution of a quantum system
subjected to a sequence of observations. These measurements occur randomly at a
given rate and can be of a very general form. As an example, we analyse the
effects of these measurements on the evolution of a two-level atom driven by an
electromagnetic field. For the associated quantum trajectories we find Rabi
oscillations, Zeno-effect type behaviour and random telegraph evolution spawned
by mini quantum jumps as we change the rates and strengths of measurement.
