The relativistic distribution for indistinguishable events is considered in the mass shell limit m2 equivalent to M2, Where M is a given intrinsic property of the events. The characteristic thermodynamic quantities are calculated and subject to the zero-mass and the high-temperature limits. The results are shown to be in agreement with the corresponding expressions of an on-mass-shell relativistic kinetic theory. The Galilean limit c to infinity , which coincides in form with the low-temperature limit, is considered. The theory is shown to pass over to a non-relativistic statistical mechanics of indistinguishable particles.