Let ((X, mathscr{A}, mu)) be a finite measure space and let (u in mathcal{L}^{1}(mu)) be strictly positive

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Let $(X, \mathscr{A}, \mu)$ be a finite measure space and let $u \in \mathcal{L}^{1}(\mu)$ be strictly positive with $\int u d \mu=1$. Show that

\[\int(\log u) d \mu \leqslant \mu(X) \log \left(\frac{1}{\mu(X)}ight)\]

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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 01:02 AM

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Let ((X, mathscr{A}, mu)) be a finite measure space and let (u in mathcal{L}^{1}(mu)) be strictly positive

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We remark that y logy is concave Theref...View the full answer

Measures Integrals And Martingales

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