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Some extensions of an inequality of Vapnik and Chervonenkis. (English) Zbl 1008.60035

Summary: The inequality of Vapnik and Chervonenkis controls the expectation of the function by its sample average uniformly over a VC-major class of functions taking into account the size of the expectation. Using Talagrand’s kernel method we prove a similar result for the classes of functions for which Dudley’s uniform entropy integral or bracketing entropy integral is finite.

MSC:

60E15 Inequalities; stochastic orderings
28A35 Measures and integrals in product spaces
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