All Lagrangians are assumed to be contained in a fixed bounded region of $X$, homologous to $L_{0}$, and are quantitatively almost calibrated. If $L_{i}$ is a sequence of exact Lagrangians with potential $f_{L_{i}}$, such that $f_{L_{i}}$ are uniformly bounded in $L^{\infty}$. Then up to subsequence, there is a Lagrangian $L$ with potential $f_{L}$, such that $L_{i}\to L$ and $f_{L_{i}}L_{i}\to f_{L}L$ as currents.