Independent random partial matching with general types

We provide a mathematical foundation for an independent random partial matching with a continuum of agents, where the type space is not necessarily finite. Besides establishing the existence result, we also identify the deterministic distributions of matched types in the matching. Our results are based on the Fubini property for Loeb product spaces and products of Loeb transition probabilities, as well as Keisler's homogeneity theorem for Loeb counting probability spaces.