  We consider a group of Bayesian agents who are each given an independent
signal about an unknown state of the world, and proceed to communicate with
each other. We study the question of asymptotic learning: do agents learn the
state of the world with probability that approaches one as the number of agents
tends to infinity?
  We show that under general conditions asymptotic learning follows from
agreement on posterior actions or posterior beliefs, regardless of the
communication dynamics. In particular, we prove that asymptotic learning holds
for the Gale-Kariv model on undirected networks and non-atomic private beliefs.
