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

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Measures Integrals And Martingales

ISBN: 9781316620243

2nd Edition

Authors: René L. Schilling

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Question Posted: Jan 25, 2024 01:04 AM

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

Question:

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

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Assume first that 251 holds ie that ...View the full answer

Measures Integrals And Martingales

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