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October, 1972 A Note on Fine and Tight Qualitative Probabilities
Ilkka Niiniluoto
Ann. Math. Statist. 43(5): 1581-1591 (October, 1972). DOI: 10.1214/aoms/1177692390


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.


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Ilkka Niiniluoto. "A Note on Fine and Tight Qualitative Probabilities." Ann. Math. Statist. 43 (5) 1581 - 1591, October, 1972.


Published: October, 1972
First available in Project Euclid: 27 April 2007

zbMATH: 0251.60003
MathSciNet: MR350797
Digital Object Identifier: 10.1214/aoms/1177692390

Rights: Copyright © 1972 Institute of Mathematical Statistics


Vol.43 • No. 5 • October, 1972
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