Event Detail

Recent developments in generalized probability theory have renewed a debate about whether regularity (i.e., the constraint that only logical contradictions get assigned probability 0) should be a necessary feature of both chances and credences. Crucial to this debate, however, are some mathematical facts regarding the interplay between the existence of regular generalized probability measures and various cardinality assumptions. Using an old theorem due to Zermelo, we improve on several known results in the literature regarding the existence of regular generalized probability measures. These results, together with recent results in Non-Archimedean Probability Theory (NAP), give, under the Generalized Continuum Hypothesis, necessary and sufficient conditions for the existence of regular generalized probability measures defined on the whole powerset of any sample space.