Uniqueness theorems for finitely additive probabilities on quantum structures

Abstract

Abstract The proofs of uniqueness theorems, presented here, allow to extend the earlier results. For example, the following hold: let μ and ν be two finitely additive probabilities on a structure L̃ (for example, L̃ is a pseudo-effect algebra), and let μ be convex-ranged; if there exists an element a ∈ L̃ with 0 < μ(a) < 1 and such that μ(a) = μ(b) ⇒ ν(a) = ν(b) whenever b ∈ L̃, then ν = μ.