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De Finetti coherence and the product law for independent events

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Abstract

In an earlier paper the present author proved that de Finetti coherence is preserved under taking products of coherent books on two finite sets of independent events. Conversely, in this note it is proved that product is the only coherence preserving operation on coherent books. Our proof shows that the traditional definition of stochastically independent classes of events actually follows from the combination of two more basic notions: boolean algebraic independence and de Finetti coherent betting system.

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Acknowledgements

The author is grateful to the two referees for their valuable remarks and suggestions for improvement.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science “Ulisse Dini”, University of Florence, Viale Morgagni 67/A, 50134, Florence, Italy

    Daniele Mundici

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  1. Daniele Mundici
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Correspondence to Daniele Mundici.

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Mundici, D. De Finetti coherence and the product law for independent events. Synthese 196, 265–271 (2019). https://doi.org/10.1007/s11229-017-1471-3

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  • DOI: https://doi.org/10.1007/s11229-017-1471-3

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