many models postulate a continuum of agents of finitely many different types who are repeatedly randomly matched in pairs to conform certain activities (e.g. play a game) which may in turn make their types change. The random matching process is usually left unspecified , and some law of large Numbers is informally invoked to justify a deterministic approximation of the resulting stochastic system. Nevertheless, it is well-known that such "law of large numbers" may not hold in the framework. This work shows that there exist random matching processes over a continuum of agents satisfying properties which are sufficient to simplify the analysis of the stochastic system.