We consider a model with an infinite numbers of states of nature, von
Neumann - Morgenstern utilities and where agents have different prob-
ability beliefs. We show 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. How-
ever, if the individually rational utility set U is compact, we obtain an
equilibrium. We give conditions which imply the compactness of U. We
give examples of non-existence of equilibrium when these conditions do
not hold
