 that $$\label{cotainferioreq0} \sup_{u \in {\partial}B_{r_0}} P_u \left( \tau_\varepsilon ({\partial}B_{r_0} \cup (\partial \tilde{G})_{(d)}) > T\right) \leq \sup_{u \in {\partial}B_{r_0}} P_u \left( \