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Journal of the Italian Statistical Society

, Volume 1, Issue 2, pp 161–181

# Weak disintegrability as a form of preservation of coherence

• Patrizia Berti
• Pietro Rigo
Article

## 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.

## Keywords

coherence conditional probability conglomerability disintegrability finite additivity prevision statistical inference

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## Copyright information

© Societa Italiana di Statistica 1992

## Authors and Affiliations

• Patrizia Berti
• 1
• Pietro Rigo
• 1
1. 1.Dipartimento StatisticoUniversità di FirenzeFirenzeItaly

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