  Gyenis and Redei have demonstrated that any prior p on a finite algebra,
however chosen, severely restricts the set of posteriors accessible from p by
Jeffrey conditioning on a nontrivial partition. Their demonstration involves
showing that the set of posteriors not accessible from p in this way (which
they call the Bayes blind spot of p) is large with respect to three common
measures of size, namely, having cardinality c, (normalized) Lebesgue measure
1, and Baire second category with respect to a natural topology. In the present
paper, we establish analogous results for probability measures defined on any
infinite sigma algebra of subsets of a denumerably infinite set. However, we
have needed to employ distinctly different approaches to determine the
cardinality, and especially, the topological and measure-theoretic sizes of the
Bayes blind spot in the infinite case. Interestingly, all of the results that
we establish for a single prior p continue to hold for the intersection of the
Bayes blind spots of countably many priors. This leads us to conjecture that
Bayesian learning itself might be just as culpable as the limitations imposed
by priors in enabling the existence of large Bayes blind spots.
