Bracketing entropy and VC-dimension

被引：0
|
作者：
Yu. V. Malykhin
机构：
[1] Russian Academy of Sciences,Steklov Mathematical Institute
来源：
Mathematical Notes | 2012年 / 91卷
关键词：
bracketing entropy; pseudodimension; VC-dimension; measurable function; bracketing compactness of sets; random variable; probability space;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We study the relationship between two characteristics of functional classes, pseudodimension and bracketing entropy. (Pseudodimension is a generalization of VC-dimension to classes of functions. Bracket entropy characterizes the L1-error of one-sided approximation of a class by finite sets.) It is shown that classes of continuous functions with finite pseudodimension possess a finite bracketing ɛ-entropy for any ɛ > 0. We establish a general result concerning the relationship between the VC-dimension of classes of sets and their bracketing entropy.
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页码：800 / 807
页数：7
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