Let $\{Y_i: i\in J\}$ be zero mean independent complex-valued random variables satisfying $|Y_i|\le R.$ Then for all $c>0,$
$$P\left(|\sum_{i\in J}Y_i|>c\right)\le 4\exp\left(\frac{-c^2}{4R^2|J|}\right).$$
See, Hoeffding, W, Probability inequalities for sums of bounded random variables, Journal of the American Statistical Asociation, 58 (1963):13-30
or P. Shmerkin Salem sets with no arithmetic progressions, international Mathematiics Research Notices.
原文：http://www.cnblogs.com/jinjun/p/6820240.html