  It thus seems eminently plausible, by the fact that this discussion immediately precedes the formulation of the ergodic hypothesis, that the intended reading of the ergodic hypothesis is really what the Ehrenfests dubbed the quasi-ergodic hypothesis, namely, the assumption that the trajectory lies densely (i.e. passes arbitrarily close to every point) on the energy  hypersurface.[10]  The quasi-ergodic hypothesis is not mathematically impossible in higher-dimensional phase spaces. However, the quasi-ergodic hypothesis does not entail the desired conclusion that the only stationary probability distribution over the energy surface is micro-canonical. One might then still conjecture that if the system is quasi-ergodic, the only continuous stationary distribution is microcanonical. But even this is fails in general (Nemytskii and Stepanov 1960). 