New Vapnik and Chervonenkis type concentration inequalities are derived for the empirical distribution of an independent random sample. Focus is on the maximal deviation over classes of Borel sets within a low probability region. The constants are explicit, enabling numerical comparisons.

翻译：新Vapnik 和 Chervonenkis 类浓度不平等是用来对独立随机抽样进行经验分布的。焦点是低概率区域内Borel 类的最大偏差。常数是明确的,便于进行数字比较。