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David Williams' Probability with Martingales has a few examples:
A simple way to obtain $\prod_{k=1}^{\infty}\frac{1}{1-p_k^{-s}}=\sum_{n=1}^{\infty}\frac{1}{n^s}$
How to prove that events A_p are independent, p is prime?
Probability of highest common factor in Williams
