关键词: Uniform convergence, non-VC class of functions, variable transformation method

Abstract: In this paper, we present a sufficient condition for uniform convergence of means to their expectations over the classes of real functions.Our proof is very simple via connecting this convergence to uniform convergence over the class of indicator functions. Furthermore, we obtain a convergent result concerning a non=VC class with an application to variable transformation for fitting regression model.

Key words: Uniform convergence, non-VC class of functions, variable transformation method