Notre Dame Journal of Formal Logic 60 (3):551-558 (2019)

Alexander R. Pruss
Baylor University
The Adams Thesis holds for a conditional → and a probability assignment P if and only if P=P whenever P>0. The restriction ensures that P is well defined by the classical formula P=P/P. Drawing on deep results of Maharam on measure algebras, it is shown that, notwithstanding well-known triviality results, any probability space can be extended to a probability space with a new conditional satisfying the Adams Thesis and satisfying a number of axioms for conditionals. This puts significant limits on how far triviality results can go.
Keywords conditional probability   measure algebra   measure theory   probability  conditionals
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DOI 10.1215/00294527-2019-0019
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