On a characterization of classical and nonclassical probabilities

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Abstract
In this paper a comparison of various approaches to the problem of characterization of probabilities is presented. The notion of multidimensional probability or S‐probability is introduced and it is shown that this notion can be profitably used for characterization of probability systems. The main results are given in Theorems 3 and 4. In Theorem 3 the conditions are considered under which a system of S‐probabilities admits a model on a generalized event space, while in Theorem 4 the conditions under which the system admits a classical model are considered. An interpretation for S‐probabilities is discussed and it is shown that Theorems 3 and 4 allow one to derive the logical structure of events from the observed probabilities.

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