Given a set ω, a finitely additive probability measure \mu on P(ω) is considered. Let \mu be "strongly" non-atomic: we prove that there exists a sequence (F<sub>n</sub>) of subsets of ω (mutually disjoint and with \mu ({F<sub>n</sub>} >0)) whose union has measure equal to an arbitrarily given 𝛼 (with 0< 𝛼 ≤ \mu(ω)=1) and such that \mu is countably additive on them. As a simple corollary, the following property (well-known for countably additive measures)is deduced: the range of \mu is the whole interval [0,1]. In the last part of the paper, some aspects of a decomposition theorem by B. De Finetti (for an arbitrary \mu) are deepened.

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