Let ((X, mathscr{A}, mu)) be a measure space and (u in mathcal{M}^{+}(mathscr{A})). Show that (A mapsto int

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 Let \((X, \mathscr{A}, \mu)\) be a measure space and \(u \in \mathcal{M}^{+}(\mathscr{A})\). Show that \(A \mapsto \int \mathbb{1}_{A} u d \mu, A \in \mathscr{A}\), is a measure.

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