Abstract
Two sub-σ-fields of a probability space are close in the Bayesian variation norm topology if there is an ex ante high probability that after conditioning, the associated posterior distributions will be close in variation norm. Stinchcombe (Journal of Mathematical Economics 19, 1990) worked with probability spaces having a countably generated σ-field and proper regular conditional probabilities. In this context, the Bayesian variation norm topology was shown to be at least as fine as the Boylan (Annals of Mathematical Statistics 42, 1971) topology. This paper establishes the equivalence of the Bayesian variation norm and the Boylan topologies. The continuity of the join operation in the Boylan topology is an immediate corollary.
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