 set in $L^{p,\,\lambda}(L^0([0,\,0]),\,l^{0};\,\mathbb{R}^n,\,w)$, and for any $\vec{f}$, $\vec{g}\in \mathcal{G}$, $$\|\Phi_{\epsilon}(\vec{f})-\Phi_{\epsilon}(\vec{g})\|_{L^{p,\,\lambda}(L^0([0,\,0]),\,l^{0};\,\mathbb{R}^n,\,w)}