Suppose that $M^2$ is a closed Riemannian manifold and that $u$ is a $C^2(M\setminus S),$ where $S$ is a measure set consisting on a possibly enumerable set of points, i.e, $u$ is equal to a $C^2$ function on almost every point on $M$. Can we still conclude that $\int_M\Delta u =0?$