 Sean Walsh has described an extension of the Brier score to the case in which the set of propositions to which we assign credences is countably infinite; and he has shown that non-probabilistic credence functions on such sets are accuracy dominated relative to that inaccuracy measure, while probabilistic ones aren’t. (For a description of Walsh's unpublished work, see Kelley 2019). Mikayla Kelley (2019) has then gone considerably further and generalized Walsh’s results significantly by describing a wide range of possible inaccuracy measures and characterizing the undominated credence functions defined on sets of propositions of different varieties. One interesting consequence is that an accuracy dominance argument for the norm of Countable Additivity does not seem to be forthcoming.