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$\begingroup$ Isn't it the case that $E[X|\mathscr{G}]$ is unique in your final exercise, because $\mathscr{G}$ is finite? There can be no question of changing $E[X|\mathscr{G}]$ on a nonempty set of measure zero w.r.t. $\mathscr{G}$. $\endgroup$

whuber
– whuber ♦

2013-11-01 22:45:50 +00:00
Commented Nov 1, 2013 at 22:45

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