Let ((X, mathscr{A}, mu)) be a measure space and (u in mathcal{M}(mathscr{A})). Show that [u in mathcal{L}^{1}(mu)

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Let $(X, \mathscr{A}, \mu)$ be a measure space and $u \in \mathcal{M}(\mathscr{A})$. Show that

\[u \in \mathcal{L}^{1}(\mu) \Longleftrightarrow \sum_{n \in \mathbb{Z}} 2^{n} \mu\left\{2^{n} \leqslant|u|<2^{n+1}ight\}<\infty\]

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Measures Integrals And Martingales

ISBN: 9781316620243

2nd Edition

Authors: René L. Schilling

Question Posted: Jan 23, 2024 10:01 AM

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Let ((X, mathscr{A}, mu)) be a measure space and (u in mathcal{M}(mathscr{A})). Show that [u in mathcal{L}^{1}(mu)

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means that we may assume that u 0 Since F...View the full answer

Measures Integrals And Martingales

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