A limit theorem on the core of an economy

In his Mathematical Psychics [5], Edgeworth presented a remarkable study of the exchanges of two commodities that might arise in an economy with two types of consumers. The first case that he considers concerns two individuals each of whom initially possesses certain quantities of each commodity. The result of trading consists of a reallocation of the total amounts of the two commodities and may, therefore, be described geometrically by a point in the Edgeworth box corresponding to that economy.