Let ((X, mathscr{A}, mu)) be a measure space and (u in mathcal{L}^{1}(mu)). Show that for every (epsilon>0)

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Let $(X, \mathscr{A}, \mu)$ be a measure space and $u \in \mathcal{L}^{1}(\mu)$. Show that for every $\epsilon>0$ there is some $\delta>0$ such that

\[
A \in \mathscr{A}, \mu(A)<\delta \Longrightarrow\left|\int_{A} u d \muight| \leqslant \int_{A}|u| d \mu<\epsilon
\]

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Measures Integrals And Martingales

ISBN: 9781316620243

2nd Edition

Authors: René L. Schilling

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Question Posted: Jan 27, 2024 12:00 PM

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Let ((X, mathscr{A}, mu)) be a measure space and (u in mathcal{L}^{1}(mu)). Show that for every (epsilon>0)

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Data from theorem 112 i ii We get udul lul du straight from the triangle inequality ...View the full answer

Measures Integrals And Martingales

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