Abstract
Savage (1954) has shown that fine and tight qualitative probabilities are realizable by finitely additive probability measures. His proof for this result is, however, in need of a correction. Fine qualitative probabilities are either atomless or equivalent to the union of $n$ equivalent atoms. Tight qualitative probabilities are always atomless. Qualitative probability structures, which are equivalent to the union of $n$ equivalent atoms, are realizable by a unique probability measure. Fine qualitative probabilities are almost realizable. With these results, the proof for Savage's theorem can be worked out and a theorem of Villegas (1964) can be strengthened.
Citation
Ilkka Niiniluoto. "A Note on Fine and Tight Qualitative Probabilities." Ann. Math. Statist. 43 (5) 1581 - 1591, October, 1972. https://doi.org/10.1214/aoms/1177692390
Information