We show an extension of Sanov's theorem on large deviations, controlling the tail probabilities of i.i.d. random variables with matching concentration and anti-concentration bounds. This result has a general scope, applies to samples of any size, and has a short information-theoretic proof using elementary techniques.

翻译：我们用大偏差来显示Sanov 理论的延伸, 控制i. id. 随机变量的尾部概率, 与浓度和抗浓缩界限相匹配。 其结果具有一般范围, 适用于任何大小的样本, 并且使用基本技术, 拥有简短的信息理论证明 。