  Considering any Hamiltonian, any initial state, and measurements with a small
number of possible outcomes compared to the dimension, we show that most
measurements are already equilibrated. To investigate non-trivial equilibration
we therefore consider a restricted set of measurements. When the initial state
is spread over many energy levels, and we consider the set of observables for
which this state is an eigenstate, most observables are initially out of
equilibrium yet equilibrate rapidly. Moreover, all two-outcome measurements,
where one of the projectors is of low rank, equilibrate rapidly.
