Metric entropies of sets in abstract Wiener space (Q2572178)

If \((X,H,\mu)\) is an abstract Wiener space, the author first recalls the definition of the metric entropy \(E(\varepsilon,K)\) of a set \(K\subset X\). Then he proves that \(\varepsilon^2 E(\varepsilon,K)\) is bounded below as \(\varepsilon\downarrow0\) when \(K\) is not a slim set, and is bounded above when \(K\) is compact and contained in the \(X\)-closure of an \(H\)-ball.