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faculty: "FEB" and publication year: "1981"
| Author||P.P. Wakker|
|Title||Clarification of some mathematical misunderstandings about Savage's foundation of statistics, 1954|
|Journal||Annals of statistics|
|Faculty||Faculty of Economics and Business|
|Institute/dept.||FEB: Research Institute in Economics and Econometrics Amsterdam (RESAM)|
|Keywords||Decision-making uner risk and uncertainty; Mathematical methods|
|Abstract||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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