An expository note on individual risk without aggregate uncertainty (Q759623)

In economies where agents bear some risk, the analysis would often be facilitated by the assumption that the risks are i.i.d. and disappear in the aggregate. A formal appeal to the law of large numbers requires the consideration of a sequence of finite economies. In an economy with a continuum of agents there are countable families of sets for which it is impossible for a law of large numbers to be valid. With countably many agents and a finitely additive measure, independence is compatible with the law of large numbers.