Let ((X, mathscr{A}, mu)) be a measure space and assume that (u in mathcal{M}(mathscr{A})) and (u=w) almost

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Let \((X, \mathscr{A}, \mu)\) be a measure space and assume that \(u \in \mathcal{M}(\mathscr{A})\) and \(u=w\) almost everywhere w.r.t. \(\mu\). When can we say that \(w \in \mathcal{M}(\mathscr{A})\) ?

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