  We show that for arbitrary linearly ordered set $X$ any bounded family of
(not necessarily, continuous) real valued functions on $X$ with bounded total
variation does not contain independent sequences. We obtain generalized Helly's
sequential compactness type theorems. One of the theorems asserts that for
every compact metric space $(Y,d)$ the compact space $BV_r(X,Y)$ of all
functions $X \to Y$ with variation $\leq r$ is sequentially compact in the
pointwise topology. Another Helly type theorem shows that the compact space
$M_+(X,Y)$ of all order preserving maps $X \to Y$ is sequentially compact where
$Y$ is a compact metrizable partially ordered space in the sense of Nachbin.
