Abstract: Firstly，random rough theory is introduced.Secondly some concepts such as random rough empirical risk functional，random rough expected risk functional and random rough empirical risk minimization principle are proposed.Finally the key theorem of statistical learning theory based on random rough samples is proved，and the bounds on the rate of uniform convergence of learning process are discussed.

Key words: random rough samples, statistical learning theory, random rough empirical risk minimization principle, the key theorem, the bounds on the rate of uniform convergence

摘要： 介绍随机粗糙理论的基本内容。提出随机粗糙经验风险泛函，随机粗糙期望风险泛函，随机粗糙经验风险最小化原则等概念。最后证明基于随机粗糙样本的统计学习理论的关键定理并讨论学习过程一致收敛速度的界。

关键词: 随机粗糙样本, 统计学习理论, 随机粗糙经验风险最小化原则, 关键定理, 一致收敛速度的界