$\mathbf{M}$ is $\mathbf{F}$ lower semicontinuous on $\mathscr{D}_m$

Question

I am working on a problem in Frank Morgan's Geometric Measure Theory book.

What I have done so far:

$T_i \to T$ under the real flat norm: $\forall \epsilon>0, \exists N$ such that $\min \{ \mathbf{M}(A-A_i) + \mathbf{M}(B-B_i)\} < \epsilon, \; \forall i \geq N$.

From here, I am stuck. How do I get to $\mathbf{M}(T) \leq \liminf \mathbf{M}(T_i)$?

First of all, am I working in the right direction? Any type of hint/help will be appreciated.