  Functions, uniformly bounded in $BV$ norm in some bounded open set $U$ in
$R^n$, are compact in $L_1(U)$. This result is known when $U$ has Lipschitz
boundary [EG Th. 4 p. 176], [G 1.19 Th. p. 17], [Z 5.34 Cor. p. 227]; the proof
for general $U$ here, after identifying the operator theoretic definition of
bounded $BV$ norm with that of the Tonelli variation, appeals to the standard
compactness criterion in $L_1$ [DS 21 TH. p. 301] [Y, p. 275] (For
completeness, these two auxiliary results are also presented).
