Abstract: <br /> Almost all work on empirical processes, so far, <br /> concerned i.i.d. <br /> data. To my knowledge, the non independent case is almost neglected and <br /> essentially <br /> restricted to ergodic sequences. In this talk, convergence in distribution <br /> (under uniform distance) of empirical processes, based on non ergodic data, <br /> is investigated. I focus on <br /> conditionally identically distributed sequences of <br /> random variables. This type of dependence, more general than <br /> exchangeability, plays a role in <br /> Bayesian predictive inference. Some foundational problems, connected to <br /> convergence in distribution of non measurable random elements, are also <br /> discussed. Among other things, necessary and sufficient conditions for <br /> convergence in distribution of empirical processes for exchangeable data <br /> are given.