Let ((X, mathscr{A})) be a measurable space and assume that (mu: mathscr{A} ightarrow[0, infty]) finitely additive and

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Let \((X, \mathscr{A})\) be a measurable space and assume that \(\mu: \mathscr{A} ightarrow[0, \infty]\) finitely additive and \(\sigma\)-subadditive. Show that \(\mu\) is \(\sigma\)-additive.

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