Asset market equilibrium with short-selling and a continuum of number of states of nature

We consider an economy with a continuum number of states of nature, von Neumann-Morgenstern utilities, where agents have different probability beliefs and where short sells are allowed. We know that no-arbitrage conditions, defined for finite dimensional asset markets models, are not sufficient to ensure existence of equilibrium in presence of an infinite number of states of nature. However, if we give conditions which imply the compactness of U, the individually rational utility set, we obtain an equilibrium. We give conditions which imply the compactness of U. This paper extends to the case of a continuum number of states no-arbitrage conditions in the literature