David Williams Probability With Martingales Solutions Best Instant

Let X, Y be independent r.v.s. Prove E[X|σ(Y)] = E[X].

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As one delves into "Probability with Martingales," they'll encounter essential concepts, such as: Let X, Y be independent r

Williams loves counterexamples (e.g., martingales that converge in probability but not in L1cap L to the first power

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$$\mathbbE[X_n+1] = \mathbbE[\mathbbE[X_n+1 | \mathcalF_n]] = \mathbbE[X_n]$$

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