\, \operatorname*{arg\,max}_{t \in {Q}} f(t) \text{ is not unique}\right\}\\
     \cup{} & \left\{f \in C({Q}\oplus L): \, f\big(\tau_{Q}(f|_{Q}) + \cdot\big) \big/ f(\tau_{Q}(f|_{Q})) \in \partial B\right\}
  \end{aligned}$$ (Lemma \[lem:interCB\] and Lemma \[lem:CB\]). Thus, by , we can assess $$\begin{aligned}
   \mu(\partial (C_B \cap A_L)) \leq{} & \mu(\partial A_L) + \mu(\partial C_B \cap A_L) \notag\\
   \leq{} & c(L) + \int_{{\mathbb R}^d \setminus ({Q}\oplus L)} \int_{\lambda^{-1}}^\infty u^{-2} 
   \sP\left\{u  \max_{t_0 \in {Q}} F(t_0 -x) \geq 1\right\}\sd u \sd x \notag\\
          & \hspace{0.7cm}  + \int_{{Q}} \int_{\lambda^{-1}}^\infty u^{-2} \sP(F / \lambda \in \partial B) \sd u \sd t \quad
       {}={} \quad 2 c(L). \label{eq:partCB}
  \end{aligned}$$

Furthermore, we get $$\begin{aligned}
   & \mu(C_B \cap A_L) \nonumber \\
   ={} & \int_{Q}\int_{\lambda^{-1}}^\infty u^{-2} \sP\Big\{F(\cdot) / \lambda \in B\Big\} 
   \sd u \sd t_0 \nonumber \\
   &  + \int_{{\mathbb R}^d \setminus({Q}\oplus L)} \int_{\lambda^{-1}}^\infty u^{-2} 
   \sP\bigg\{u  \max_{t_0 \in {Q}} F(t_0 -x) \geq 1,\ \nonumber \\
   &     \hspace{2.5cm} 
   F\left(\Big(\tau_{Q}(F(\cdot-x)|_{Q})\Big)+\cdot-x\right) \Big/ \max_{t_0 \in {Q}} F(t_0-x) \in B,\nonumber \\
   &     \hspace{2.5cm} F(t-x) / \max_{t_0 \in {Q}} F(t_0-x) \leq 1 
   \ \forall t \in {Q}\oplus L \bigg\} \sd u \sd x. \label{eq:CB}
 \end{aligned}$$ The second term in is positive and can be bounded from above by $c(L)$. Setting $B= C(K)$, $\mu(A_L)$ can be expressed in an analogous way. Now, 