= Metric covering number
{title2=$N(\varepsilon,T,d)$}
= Covering number
{synonym}
For a <metric space> or <pseudometric> space $(T,d)$, this is the minimum number of balls of radius $\varepsilon>0$, with centers in $T$, needed to cover $T$. The displayed grid bound uses closed balls. For open balls, replacing the radius by a fixed constant factor gives the same entropy estimates. For $T=[0,1]$ and $d(s,t)=c|s-t|^H$, a uniform grid gives $N(\varepsilon,T,d)\leq1+\lceil(c/\varepsilon)^{1/H}\rceil$. These polynomial growth bounds make the <Dudley entropy integral> finite.
Back to article page
