关键词: 泛空间, 泛随机变量, 噪声, 经验风险最小化原则, 关键定理

Abstract: The key theorem plays an important role in the statistical learning theory. However, the researches about it at present focus on probability space and the samples are supposed to be noise-free. In consideration of these facts, the definitions of expected risk functional, empirical risk functional and empirical risk minimization principle with samples corrupted by noise on pan-space are proposed, and the key theorem of learning theory with samples corrupted by noise on pan-space is proposed and proved.

Key words: pan-space, pan-random variable, noise, empirical risk minimization principle, key theorem