Finitely additive conditional probabilities with values on a hyperstructure
Antonio Maturo · Journal of Information and Optimization Sciences · 2001
In this paper we introduce a particular non standard algebraic hyperstructure ∑ with two hyperoperations called addition and multiplication that is an extension of the field of real numbers. After we define probabilities and conditional probabilities with values on ∑. In this way we can assign non null probabilities to events that have null standard probabilities. We prove that, with such hyperstructure, many problems about the conditional probability (e.g. coherence) can have easy and smart solutions. There-fore, with such generalized probability, we can assume that, in a generalized sense, the classical definition of conditional probability agrees with the one of de Finetti.