  This note establishes that if a sequence $P_n, n=1,\ldots$ of probability
measures converges in total variation to the limiting probability measure $P$,
and $\sigma$-algebras $\mathbb{A}$ and $\mathbb{B}$ are conditionally
independent given $\mathbb{H}$ with respect to $P_n$ for all $n$, then they are
also conditionally independent with respect to the limiting measure $P$. As a
corollary, this also extends to pointwise convergence of densities to a
density.
