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Theory of probability. A critical introductory treatment. Volume 1 and 2. Transl. by Antonio Machi and Adrian Smith. Reprint. (English) Zbl 0694.60001

Wiley Classics Library. Chichester etc.: John Wiley & Sons. xix, 300 p./vol.1; xviii, 375 p./ vol.2 £19.95/each vol. (1990).
[For a review of the English original edition see Zbl 0328.60002 resp. Zbl 0328.60003.]
As D. Lindley writes in the foreword, “this book is not a text on probability in the ordinary sense” and “is destined ultimately to be recognized as one of the great books of the world”.
The first volume covers the logic of certainty (events, linear representations of random quantities) and uncertainty (prevision and probability, also conditional ones), evaluations of probabilities, distributions. The second volume deals with stochastic processes, problems in higher dimensions, statistical inference, and closes with a long appendix in which many topics already discussed in the book are reconsidered in greater detail.
It is impossible to synthesize in a short review the unusual features of this masterpiece in the theory of subjective probability: often it contains original and interesting digressions, even during the proof of a statement; but the possible further work required to follow these digressions is always largely rewarded by a stimulating and unifying view of the deeper aspects.
Reviewer: R.Scozzafava

MSC:

60-02 Research exposition (monographs, survey articles) pertaining to probability theory
60Gxx Stochastic processes
62-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics
60Axx Foundations of probability theory
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