  We study the canonical weak distributive law $\delta$ of the powerset monad
over the semimodule monad for a certain class of semirings containing, in
particular, positive semifields. For this subclass we characterise $\delta$ as
a convex closure in the free semimodule of a set. Using the abstract theory of
weak distributive laws, we compose the powerset and the semimodule monads via
$\delta$, obtaining the monad of convex subsets of the free semimodule.
