  In this paper, we consider asymptotically flat Riemannnian manifolds
$(M^n,g)$ with $C^0$ metric $g$ and $g$ is smooth away from a closed bounded
subset $\Sigma$ and the scalar curvature $R_g\ge 0$ on $M\setminus \Sigma$. For
given $n\le p\le \infty$, if $g\in C^0\cap W^{1,p}$ and the Hausdorff measure
$\mathcal{H}^{n-\frac{p}{p-1}}(\Sigma)<\infty$ when $n\le p<\infty$ or
$\mathcal{H}^{n-1}(\Sigma)=0$ when $p=\infty$, then we prove that the ADM mass
of each end is nonnegative. Furthermore, if the ADM mass of some end is zero,
then we prove that $(M^n,g)$ is isometric to the Euclidean space by showing the
manifold has nonnegative Ricci curvature in RCD sense. This extends the result
of [Lee-LeFloch2015] from spin to non-spin, also improves the result of
[Shi-Tam2018] and [Lee2013]. Moreover, for $p=\infty$, this confirms a
conjecture of Lee [Lee2013].
