  In how far does an non-equilibrium initial ensemble evolve towards a
stationary long time behavior for an isolated macroscopic quantum system? We
demonstrate that deviations from a steady state indeed become unmeasurably
small or exceedingly rare after initial transients have died out under the
following conditions: The Hamilonian does not exhibit exceedingly large
degeneracies of energy eigenvalues and energy gaps. A large number of energy
levels is significantly populated by the initial ensemble. The system is
observed by a measurement device with a reasonably bound working range compared
to the resolution limit. The entire experiment, ending with the quantum
mechanical measurement process, can only be repeated a "reasonable" number of
times. It is argued that all these prerequisites for equilibration are
fulfilled under many, if not all, experimentally realistic conditions.
