Let (mu) and (u) be measures on the measurable space ((X, mathscr{A})). Show that the absolute continuity

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Let \(\mu\) and \(u\) be measures on the measurable space \((X, \mathscr{A})\). Show that the absolute continuity condition (25.1) is equivalent to

\[\mu(A \triangle B)=0 \Longrightarrow u(A)=u(B) \quad \text { for all } A, B \in \mathscr{A}\]

Equation 25.1

NEA, (N)=0v(N)=0. (25.1)

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