That is the ultimate goal. David Williams did not write "Probability with Martingales" to torture you. He wrote it to transform you into an independent thinker in measure-theoretic probability. The best solutions are merely the scaffold that helps you build that mind.
Beyond teaching, Williams wrote solutions—careful, annotated, and practical. He preferred constructions that revealed why a result held, not just that it did. For a tricky problem asking to show that a uniformly integrable martingale converges almost surely and in L1, his solution began with basic lemmas: show convergence in probability using maximal inequalities, then upgrade with uniform integrability to L1. He annotated each step with the intuition: control tail mass, squeeze out oscillation, and lock convergence with integrability. david williams probability with martingales solutions best
Often includes modern notation and corrections for known typos in the text. 2. University Course Pages That is the ultimate goal