  Many economic models include random shocks imposed on a large number
(continuum) of economic agents with individual risk. In this context, an exact
law of large numbers and its converse is presented in Sun (2006) to
characterize the cancelation of individual risk via aggregation. However, it is
well known that the Lebesgue unit interval is not suitable for modeling a
continuum of agents in the particular setting. The purpose of this paper is to
show that an extension of the Lebesgue unit interval does work well as an agent
space with various desirable properties associated with individual risk.
