  We study the solutions to a nonlocal 1-Laplacian equation given by $$
2\text{P.V.}\int_{\mathbb{R}^N}\frac{u(x)-u(y)}{|u(x)-u(y)|}
\frac{dy}{|x-y|^{N+s}}=f(x) \quad \textmd{for } x\in \Omega, $$ with Dirichlet
boundary condition $u(x)=0$ in $\mathbb R^N\backslash \Omega$ and nonnegative
$L^1$-data. By investigating the asymptotic behaviour of renormalized solutions
$u_p$ to the nonlocal $p$-Laplacian equations as $p$ goes to $1^+$, we
introduce a suitable definition of solutions and prove that the limit function
$u$ of $\{u_p\}$ is a solution of the nonlocal $1$-Laplacian equation above.
