Bracketing entropy and VC-dimension (Q2435838)

Let \(\mathcal F\) be a class of continuous functions on \([0,1]\), bounded by some integrable function. It is shown that if \(\mathcal F\) has finite pseudodimension, where pseudodimension is a generalization of the concept of Vapnik-Chervonenkis dimension to classes of functions, then the bracketing \(\varepsilon\)-entropy of \(\mathcal F\) is finite for every \(\varepsilon>0\).