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