  We demonstrate by simple mathematical considerations that a power-law tailed
distribution in the kinetic energy of relativistic particles can be a limiting
distribution seen in relativistic heavy ion experiments. We prove that the
infinite repetition of an arbitrary composition rule on an infinitesimal amount
leads to a rule with a formal logarithm. As a consequence the stationary
distribution of energy in the thermodynamical limit follows the composed
function of the Boltzmann-Gibbs exponential with this formal logarithm. In
particular, interactions described as solely functions of the relative
four-momentum squared lead to kinetic energy distributions of the
Tsallis-Pareto (cut power-law) form in the high energy limit.
