(Allard compactness [4]) Let $L_{i}$ be a sequence of $m$-dimensional integer rectifiable varifolds in a complete Riemannian manifold $X$, all supported in a fixed bounded subset, with a uniform volume upper bound $\text{Mass}(L_{i})\leq C$ and a uniform bound on the first variation $\int_{L_{i}}|\vec{H}|\leq C$. Then up to subsequence, $L_{i}$ converges to an $m$-dimensional integer rectifiable varifold $L$ with the same bounds.