The bounds of learning processes on possibility space

Statistical learning theory on probability space is an important part of machine learning. Based on the key theorem, the bounds on the rate of relative uniform convergence have significant meaning. These bounds determine generalization ability of the learning machines utilizing the empirical risk minimization induction principle. In this paper, the bounds of the learning processes on possibility space are discussed, and the rate of relative uniform convergence is estimated, and finally the relation between the rate of convergence and the capacity of a set of function is pointed out.