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ε-Entropy and moduli of smoothness in L p -spaces

A. Kamont (1992)

Studia Mathematica

The asymptotic behaviour of ε-entropy of classes of Lipschitz functions in L p ( d ) is obtained. Moreover, the asymptotics of ε-entropy of classes of Lipschitz functions in L p ( d ) whose tail function decreases as O ( λ - γ ) is obtained. In case p = 1 the relation between the ε-entropy of a given class of probability densities on d and the minimax risk for that class is discussed.

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