2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71231The 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.12 pagesProbability60G20text