Show that (mathbb{E}^{mathscr{G}} 1=1) if, and only if, (left.muight|_{mathscr{G}}) is (sigma)-finite. Find a counterexample showing that (mathbb{E}^{mathscr{G}}

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Show that $\mathbb{E}^{\mathscr{G}} 1=1$ if, and only if, $\left.\muight|_{\mathscr{G}}$ is $\sigma$-finite. Find a counterexample showing that $\mathbb{E}^{\mathscr{G}} 1 \leqslant 1$ is, in general, the best possible.

[use $p=2$ and $\mathbb{E}^{\mathscr{G}}=\mathbb{E}^{\mathscr{G}}$.]

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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 01:07 AM

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Show that (mathbb{E}^{mathscr{G}} 1=1) if, and only if, (left.muight|_{mathscr{G}}) is (sigma)-finite. Find a counterexample showing that (mathbb{E}^{mathscr{G}}

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Mind the typo in the hint E E should read E E Assume first that le is ofinite and denote by G...View the full answer

Measures Integrals And Martingales

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