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There are many diverse examples of groups with a large number of competing participants.Following pioneering contributions of von Neumann and Morgenstern (1944), Milnor and Shapley (1961), and Aumann (1964), it has become common to use a non-atomic measure space to model the interaction of a large number of agents.This talk will show how rich measure spaces can be used not only to resolve some difficulties associated with the usual model of economies and games with many agents, but also to go beyond to discover unexpected new connections in economics as well as in mathematics.