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GLIVENKO-CANTELLI TYPE THEOREMS ANDTHEIR APPLICATIONS

GLIVENKO-CANTELLI TYPE THEOREMS AND THEIR APPLICATIONS
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摘要 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. 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.
作者 朱力行
出处 《Acta Mathematica Scientia》 SCIE CSCD 1997年第3期309-318,共10页 数学物理学报(B辑英文版)
关键词 uniform convergence non-VC class of functions variable transformation method uniform convergence non-VC class of functions variable transformation method
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