It's the conditional Bayes theorem:

Some conditions, blah blah

Then $\displaystyle \bar{E}[X|\mathcal{G}] = \frac{E[\Lambda X|\mathcal{G}]}{E[\Lambda|\mathcal{G}]}$

I'm fine with the bulk of the proof, it's just that it starts off by defining

$\displaystyle Y=\frac{E[\Lambda X|\mathcal{G}]}{E[\Lambda|\mathcal{G}]}$ if $\displaystyle E[\Lambda|\mathcal{G}]>0$ and Y = 0 otherwise

Then it says we need to show $\displaystyle Y = \bar{E}[X|\mathcal{G}]$

But I don't really see that $\displaystyle Y=\frac{E[\Lambda X|\mathcal{G}]}{E[\Lambda|\mathcal{G}]}$

In fact if $\displaystyle E[\Lambda|\mathcal{G}] = 0$ Then the RHS of the formula is undefined! So.... what's going on here? :S

Thanks for any help!