British Journal for the Philosophy of Science 40 (2):167-181 (1989)
|Abstract||Kolmogorov's account in his  of an absolute probability space presupposes given a Boolean algebra, and so does Rényi's account in his  and  of a relative probability space. Anxious to prove probability theory ‘autonomous’. Popper supplied in his  and  accounts of probability spaces of which Boolean algebras are not and  accounts of probability spaces of which fields are not prerequisites but byproducts instead.1 I review the accounts in question, showing how Popper's issue from and how they differ from Kolmogorov's and Rényi's, and I examine on closing Popper's notion of ‘autonomous independence’. So as not to interrupt the exposition, I allow myself in the main text but a few proofs, relegating others to the Appendix and indicating as I go along where in the literature the rest can be found.|
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