Summary
Weak disintegrations are investigated from various points of view. Kolmogorov's definition of conditional probability is critically analysed, and it is noted how the notion of disintegrability plays some role in connecting Kolmogorov's definition with the one given in line with de Finetti's coherence principle. Conditions are given, on the domain of a prevision, implying the equivalence between weak disintegrability and conglomerability. Moreover, weak sintegrations are characterized in terms of coherence, in de Finetti's sense, of, a suitable function. This fact enables us to give, an interpretation of weak disintegrability as a form of “preservation of coherence”. The previous results are also applied to a hypothetical inferential problem. In particular, an inference is shown to be coherent, in the sense of Heath and Sudderth, if and only if a suitable function is coherent, in de Finetti's sense.
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Research partially supported by: M.U.R.S.T. 40% “Problemi di inferenza pura”.
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Berti, P., Rigo, P. Weak disintegrability as a form of preservation of coherence. J. It. Statist. Soc. 1, 161–181 (1992). https://doi.org/10.1007/BF02589029
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DOI: https://doi.org/10.1007/BF02589029