Consider two agents who learn the value of an unknown parameter by observing a sequence of private signals. The signals are independent and identically distributed across time but not necessarily agents. Does it follow that the agents will commonly learn its value, i.e., that the true value of the parameter will become (approximate) common-knowledge? We show that the answer is aﬀirmative when each agent’s signal space is ﬁnite and show by example that common learning can fail when observations come from a countably inﬁnite signal space.
Cripps, Martin W.; Ely, Jeffrey C.; Mailath, George J.; and Samuelson, Larry, "Common Learning" (2006). Cowles Foundation Discussion Papers. 1866.