Suppose $L_{i}$ is a sequence of immersed Lagrangian branes, all in the same $D^{b}Fuk(X)$ class, and is a Cauchy sequence with respect to the distance on the branes. Suppose $L$ is an immersed Lagrangian, and $L_{i}\to L$ in the varifold/current topology. Then does there exist a suitable brane structure on $L$ so that $L_{i}\to L$ with respect to the distance on the branes?