Outer Sphere Condition

An open set \(\Omega \subset \mathbb{R}^d\) satisfies the outer sphere condition if and only if for every boundary point \(x\in \partial \Omega\) there is a point \(y\in \mathbb{R}^d\) and a radius \(r>0\) such that \(B_r(y)\cap \overline{\Omega}=\{x\}\).