  On any quaternionic manifold of dimension greater than 4 a class of
plurisubharmonic functions (or, rather, sections of an appropriate line bundle)
is introduced. Then a Monge-Amp\`ere operator is defined. It is shown that it
satisfies a version of theorems of A. D. Alexandrov and Chern-Levine-Nirenberg.
These notions and results were previously known in the special case of
hypercomplex manifolds. One of the new technical aspects of the present paper
is the systematic use of the Baston differential operators, for which we prove
a new multiplicativity property.
