 $$\label{decomp0} \lim_{\varepsilon \rightarrow 0} \left[\sup_{u \in {\partial}B_{r_0}} \frac{P_u (A \cap \{ \tau_\varepsilon^0 = \min\{ \tau_\varepsilon^0, \tau_\varepsilon^0, \tau_\varepsilon^0, \tau_\varepsilon^0 \} \})}{P_u ( Z_0^\varepsilon \in {\partial}G ) }\right] = 0.$$  ### Upper bound on $P(A \cap \{ \tau_\varepsilon^0 = \min\{ \tau_\varepsilon^0, \tau_\varepsilon^0, \tau_\varepsilon^0, \tau_\varepsilon^0 \} \})$  To bound the probability of the 