- Clarification of some mathematical misunderstandings about Savage's foundation of statistics, 1954
- The Annals of Statistics
- Pages (from-to)
- Document type
- Faculty of Economics and Business (FEB)
- Amsterdam School of Economics Research Institute (ASE-RI)
It is proved that fine and tight comparative probability structures (where the set of events is assumed to be an algebra, not necessarily a sigma-algebra) have agreeing probability measures. Although this was often claimed in the literature, all proofs the author encountered are not valid for the general case, but only for sigma-algebras. Here the proof of Niiniluoto (1972, Annals of Mathematical Statistics) is supplemented. Furthermore an example is presented that reveals many misunderstandings in the literature. At the end a necessary and sufficient condition is given for comparative probability structures to have an almost agreeing probability measure.
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