This paper describes properties of homothetic preferences on a subset X of a vector space which is star-shaped with respect to 0 (e.g., a cone). We prove that a preference relation on X is homothetic, greedy and calibrated if and only if there exists a positively homogeneous function that...

A finitely additive probability measure P defined on a class of subsets of a space is convex-ranged if, for all P(A)0 and all 0 < < 1, there exists a set, ∋ B⊆A, such that P(B)= P(A).<p>Our main result shows that, for any two probabilities P and Q, with P convex-ranged and Q countably additive, P=Q whenever there exists a set A∈ , with 0 P(A) 1,...</<>