A central result in the rational learning literature is that if the true measure is absolutely continuous with respect to the beliefs then, given enough data, the updated beliefs merge with the true distribution. In this paper, we show that, under absolute continuity, weak merging occurs fast...

Each period, one outcome out of finitely many possibilities is observed. Each period, a forecaster announces some probability for the future outcomes based on the available data. An outsider wants to know if the forecaster has some knowledge of the data generating process. Let a test be an...