The paper presents an interesting generalisation of some results about de Finetti coherent probabilities to an assignment of indeterminate probabilities on many-valued events in an MV-algebra. After recalling the Dutch Book interpretation of probability by de Finetti and his well-known related theorem, which states that an agent's degrees of belief are coherent (i.e. they do not permit a Dutch Book) if and only if they conform to probability axioms, the author proves an analogous result for upper (and lower) probabilities defined on divisible MV-algebras. Specifically, she proves that in a divisible MV-algebra of events a book does not allow any bad bet if and only if it can be extended to an upper probability over the whole MV-algebra. The proof of this result relies on Hahn-Banach and separation theorems as well as on other tools from functional analysis.
