We present versions of the two fundamental welfare theorems of economics for exchange economies with a countable number of agents and an inﬁnite dimensional commodity space. These results are then specialized to the overlapping generations model.
Aliprantis, Charalambos D.; Brown, Donald J.; and Burkinshaw, Owen, "Valuation and Optimality in Exchange Economies with a Countable Number of Agents" (1987). Cowles Foundation Discussion Papers. 1081.