The ergodic hypothesis states that, if one waits for a long enough time, the geometric locus of a representative point covers the whole phase space. In other words, the point will eventually travel through the entirety of phase space, leaving no location unvisited. This implies that the point density (which represents the Probability distribution of states) is uniform over a constant-energy hypersurface, which means that all states on that surface are equally likely. This statement is known in statistical mechanics as the equal a priori probability hypothesis.