🚀 If you're stuck on a specific exercise (like E10.1 or the "Star Trek" problem), let me know which one and I can help walk through the logic!

Problems involving $E[X|\mathcalG]$ require careful handling of "almost sure" equalities. Top-tier solutions distinguish between equality everywhere and equality a.s., and show why a candidate satisfies the two defining properties (measurability and integral matching).

If you are stuck on a specific exercise number, these forums often have step-by-step breakdowns: Williams 'Probability with martingales' E9.2