Let (mu, u) be two (sigma)-finite measures on ((X, mathscr{A})) which have the same null sets. Show

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Let \(\mu, u\) be two \(\sigma\)-finite measures on \((X, \mathscr{A})\) which have the same null sets. Show that \(u=f \mu\) and \(\mu=g u\), where \(0

Remark. Measures having the same null sets are called equivalent.

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