Metric entropies of sets in abstract Wiener space

Let (X, H μ) be an abstract Wiener space, E (ε, K) denote the metric entropy of a set K ⊂ X. If K is not a slim set, then we prove that 0 < lim inf ε→0 ε² E(ε). In particular, if lim inf_3→0 ε²E (ε, K) = 0, then K is a slim set. Moreover, if K is compact and contained in the closure of B₀^H (R) in X, where B₀^H := {h ∈ H: ∥h∥_H < R} is a ball in H, then lim supε→0 ε² E(ε, K) < ∞.