Summary
The paper shows that the set of stable probability measures and the set of Rational Beliefs relative to a given stationary measure are closed in the strong topology, but not closed in the topology of weak convergence. However, subsets of the set of stable probability measures which are characterized by uniformity of convergence of the empirical distribution are closed in the topology of weak convergence. It is demonstrated that such subsets exist. In particular, there is an increasing sequence of sets of SIDS measures who's union is the set of all SIDS measures generated by a particular system and such that each subset consists of stable measures. The uniformity requirement has a natural interpretation in terms of plausibility of Rational Beliefs.
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ncial support from The Carlsberg Foundation, The University of Copenhagen, and Danish Social Science Research Council is gratefully acknowledged. I would like to thank Trinidad Casasus, Mordecai Kurz, and Tiefeng Jiang for many useful suggestions for improving the paper, and Karl Vind for helpful discussions about parts of it.