  Drawing from our earlier works on the notion of causality for nonlocal
phenomena, we propose and study the extension of the Sorkin--Woolgar relation
$K^+$ onto the space of Borel probability measures on a given spacetime. We
show that it retains its fundamental properties of transitivity and closedness.
Furthermore, we list and prove several characterizations of this relation,
including the `nonlocal' analogue of the characterization of $K^+$ in terms of
time functions. This generalizes and casts new light on our earlier results
concerning the causal precedence relation $J^+$ between measures.
