  Functional representations of the capacity monad based on the max and min
operations were considered in \cite{Ra1} and \cite{Ny1}. Nykyforchyn considered
in \cite{Ny2} some alternative monad structure for the possibility capacity
functor based on the max and usual multiplication operations. We show that such
capacity monad (which we call the capacity multiplication monad) has a
functional representation, i.e. the space of capacities on a compactum $X$ can
be naturally embedded (with preserving of the monad structure) in some space of
functionals on $C(X,I)$. We also describe this space of functionals in terms of
properties of functionals.
