  We demonstrate equilibration of isolated many-body systems in the sense that,
after initial transients have died out, the system behaves practically
indistinguishable from a time-independent steady state, i.e., non-negligible
deviations are unimaginably rare in time. Measuring the distinguishability in
terms of quantum mechanical expectation values, results of this type have been
previously established under increasingly weak assumptions about the initial
disequilibrium, the many-body Hamiltonian, and the considered observables.
Here, we further extend these results with respect to generalized
distinguishability measures which fully take into account the fact that the
actually observed, primary data are not expectation values but rather the
probabilistic occurrence of different possible measurement outcomes.
