  The relativistic distribution for indistinguishable events is considered in
the mass-shell limit $m^2\cong M^2,$ 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 $c\rightarrow \infty ,$ which
coincides in form with the low-temperature limit, is considered. The theory is
shown to pass over to a nonrelativistic statistical mechanics of
indistinguishable particles.
