Geodesic
Bracketing Entropy and VC-Dimension
Matematičeskie zametki, Tome 91 (2012) no. 6, pp. 853-860

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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 $L_1$-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 $\varepsilon$-entropy for any $\varepsilon>0$. We establish a general result concerning the relationship between the VC-dimension of classes of sets and their bracketing entropy.
Keywords: bracketing entropy, measurable function, bracketing compactness of sets, random variable, probability space.
Mots-clés : pseudodimension, VC-dimension 
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     author = {Yu. V. Malykhin},
     title = {Bracketing {Entropy} and {VC-Dimension}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {853--860},
     publisher = {mathdoc},
     volume = {91},
     number = {6},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_91_6_a5/}
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Yu. V. Malykhin. Bracketing Entropy and VC-Dimension. Matematičeskie zametki, Tome 91 (2012) no. 6, pp. 853-860. http://geodesic.mathdoc.fr/item/MZM_2012_91_6_a5/