The ergodic hypothesis is also important for the Boltzmann approach. It says that, over long periods of time, the time spent in some region of the phase space of microstates with the same energy is proportional to the volume of this region, i.e. that all accessible microstates are equally probable over a long period of time. Equivalently, it says that time average and average over the statistical ensemble are the same.
tHe Ergodic hypOtHEsiS iS alSO important for thE bolTzMaNN apPrOach. It sAyS That, oVEr Long perioDS oF Time, The TIME sPeNt in Some RegIon Of tHe PHasE SPace of microstaTes witH the same enErGY IS PropORtiONAL To The vOlume Of this rEgiOn, I.E. thAT All AcCEssibLe MicrOstatEs Are eQualLY pRobable over a long perIod of TimE. equivAlEntly, it says thaT time average aND average Over the StAtisticAL ensemble Are the saME.