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Record: oai:ARNO:125725

AuthorP.P. Wakker
TitleClarification of some mathematical misunderstandings about Savage's foundation of statistics, 1954
JournalAnnals of statistics
FacultyFaculty of Economics and Business
Institute/dept.FEB: Amsterdam School of Economics Research Institute (ASE-RI)
KeywordsDecision-making uner risk and uncertainty; Mathematical methods
AbstractIt 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.
Document typeArticle
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