Some remarks on entropy numbers of sets with non-integer dimension

Abstract

We study entropy numbers of sets and generalize some results shown by B. Carl and I. Stephani in [2]. It is well known that if Ω is the closed unit ball in the Euclidean space R N , then for every n ∈ N,We extend estimates of this type to more general subsets of metric spaces. Moreover we study relations between the asymptotic behaviour of the entropy numbers of bounded subsets of R N and their box dimension. Mathematics Subject Classification (2000)28A80 · 28A78