We characterize ex post equilibria in uniform-price double auctions of divisible assets.  Bidders receive private signals, have interdependent and diminishing marginal values, and bid with demand schedules.  In a static double auction we characterize an ex post equilibrium, in which no bidder would deviate from his strategy even if he would observe the signals of other bidders.  Moreover, under mild conditions this ex post equilibrium is unique.  In a market with a sequence of double auctions and stochastic arrivals of new signals, we characterize a stationary and subgame perfect ex post equilibrium whose allocation path converges exponentially in time to the efficient level.  We also demonstrate that the socially optimal trading frequency depends on the arrival process of new information.  Our ex post equilibrium aggregates dispersed private information and is robust to distributional assumptions and details of auction design.