A note on the ε entropy of monotone functions in the levy norm

AbstractThe ϵ entropy of the class F∗ of real-valued monotone functions from [0, 1] to [0, 1] in the usual Chebyshev norm is infinite, due to the discontinuities in some of the f ϵ F∗. One of the class of norms introduced by P. Lévy for analyzing the convergence of distribution functions gives finite ϵ entropy ∼(1ϵ). (There is an obvious extension to the class F∗AB of monotone functions from [0, A] to [0, B]