. Now, since $\lim_{\varepsilon \rightarrow 0^+} \Delta E^{H^\varepsilon}_{\eta^\varepsilon} (\gamma^\varepsilon_x) = \Delta E^{H^0}_\eta (\gamma_x)$ for every $\eta \in \mathcal{N}(S \times G)$ and $\gamma_x \in S \times G$, it follows that there exists (random) $\varepsilon_0 > 0$ such that if $0 \leq \varepsilon < \varepsilon_0$ then $$\label{ancesinc