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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 &lt;  μ ( a ) &lt; 1 and such that  μ ( a ) =  μ ( b ) ⇒  ν ( a ) =  ν ( b ) whenever  b  ∈  L̃ , then  ν  =  μ .

Uniqueness theorems for finitely additive probabilities on quantum structures