On coherence and conditional prevision

The purpose of the paper is to continue and to reinterpret de Finetti's work on the coherence in the context of conditional previsions. We prove three basic results: the extension property, the equivalence property and the restricted equivalence property. Moreover, we show that Dubins'extension theorems for finitely additive conditional probabilities and for strategies are elementary consequences of the extension property and of the restricted equivalence property.