s to prove that, for each fixed $\epsilon>0$, there exists a $\delta=\delta_{\epsilon}>0$ and a mapping $\Phi_{\epsilon}$ on $L^{p,\,\lambda}(L^0([0,\,0]),\,l^{0};\,\mathbb{R}^n,\,w)$, such that $\Phi_{\epsilon}(\mathcal{G})=\{\Phi_{\epsilon}(\vec{f}):\,\vec{f}\in \mathcal G\}$ is a strong