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Bayes' rule for conditional expectations (Proof review)

$$ \def\Filtr{\mathcal{F}} \def\EF{E^\Filtr} $$ Let $f=dQ/dP$, and denote by $E$, $E_Q$ the expectation with respect to the measure $P$, $Q$, respectively. Let us also write $\EF$, $\EF_Q$ instead of $...
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