Abstract: Firstly，birandom theory is introduced.Secondly some concepts such as birandom empirical risk functional，birandom expected risk functional and birandom empirical risk minimization principle are proposed.Finally the key theorem of statistical learning theory based on birandom samples is proved，and the bounds on the rate of uniform convergence of learning process are discussed.The investigations will help lay essential theoretical foundations for the systematic and comprehensive development of statistical learning theory and support vector machine based on uncertain samples.

摘要： 介绍双重随机理论的基本内容。提出双重随机经验风险泛函，双重随机期望风险泛函，双重随机经验风险最小化原则等概念。最后证明基于双重随机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。为系统建立基于不确定样本的统计学习理论并构建相应的支持向量机奠定了理论基础。