  Integral representations are obtained of positive additive functionals on
finite products of the space of continuous functions (or of bounded Borel
functions) on a compact Hausdorff space. These are shown to yield
characterizations of the dual mixed volume, the fundamental concept in the dual
Brunn-Minkowski theory. The characterizations are shown to be best possible in
the sense that none of the assumptions can be omitted. The results obtained are
in the spirit of a similar characterization of the mixed volume in the
classical Brunn-Minkowski theory, obtained recently by Milman and Schneider,
but the methods employed are completely different.
