Mean field limits by population acceleration

Mean field or large population limits are useful analytical tools that provide well justified approximations to finite systems. Motivated by problems in Game Theory and Queueing Theory we provide a framework to develop mean field limits that emerge from finite population systems in a very general setting. Our results prove new generalizations of the standard Glivenko-Cantelli and Donsker´s Theorems. We prove these limits by making use of an analytical technique called population acceleration first introduced in [1] to study transtitory queueing models.