Carleson box ($S(I)=\{r\xi :\xi \in I,1-m(I)<r<1\}$)

A boundary neighborhood over an arc $I$ of the unit circle, with radial depth equal to its normalized angular length $m(I)$. Changing that depth by any fixed positive factor gives an equivalent Carleson measure condition. Large arcs and central mass can be handled separately by finitely many fixed neighborhoods covering the unit disc.