关键词: 泛空间, 泛可加测度, 经验风险最小化原则, 关键定理

Abstract: Some definitions and properties of pan-random variable and its distribution，pan-expectation and pan-variance on pan-space are introduced，and Chebyshev’inequality and the Khinchine’s strong law of large numbers on pan-space are proved.The definitions of expected risk functional，empirical risk functional and the empirical risk minimization inductive principle on pan-space are proposed，and then the key theorem of learning theory on pan-space is proved.As a result，the key theorems of learning theory on probability measure space and possibility space are unified and extended to pan-space.

Key words: pan-space, pan additive measure, the empirical risk minimization inductive principle, the key theorems