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Let $X$ be a set, $F \subset \mathcal{P}(X)$. Let $\mu: F \to \mathbb{R}$ be a finitely additive measure on $F$.

Is it possible to assume some additional properties of $\mu$, which would necessarily imply that $F$ is a algebra? If yes, what are they and how do I then show that $F$ is algebra?

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