Referring to this question on harmonic function in which is proved the sequent
Let $u(x)$ a harmonic function in $\mathbb{R}^n$ such as: \begin{equation} \int_{\mathbb{R}^n}|u(x)|dx =K< \infty \end{equation} Show thtat $u(x)=0$, $\forall x \in \mathbb{R}^n$.
Is there a heuristic argument to prove it or an explanation about why harmonic function that gives a finite value when integrated must be 0, without doing the rigorous proof?