Among other results we prove that for a Banach space $X$ and $1 < p < \infty$,
all $p$-unconditionally Cauchy sequences in $X$ lie inside the range of a
$Y$-valued measure of bounded variation for some Banach space $Y$ containing
$X$ if and only if each $\ell_1$-valued $2$-summing map on $X$ induces a nuclear
map on $X$ valued in $\ell_q$, $q$ being conjugate to $p$. We also characterise
Banach spaces $X$ with the property that all $\ell_2$-valued absolutely summing
maps on $X$ are already nuclear as those for which $X^\ast$ has
the (GT) and (GL) properties.