Acts are functions from the set of states of the world into the set of consequences. Savage proposed axioms regarding a binary relation on the set of acts which are necessary and sufftcient for it to be representable by the functional gu(.)dP for some real-valued (utility) function u on the set of consequences and a (probability) measure P on the set of states of the world. The Ellsberg paradox...

It is well known that real numbers with a purely periodic decimal expansion are rationals having, when reduced, a denominator coprime with 10. The aim of this paper is to extend this result to betaexpansions with a Pisot base beta which is not necessarily a unit. We characterize real numbers having a purely periodic expansion in such a base. This characterization is given in terms of an explici...