Characterizing the dual mixed volume via additive functionals Paolo DulioR. GardnerCarla Peri Primary: 52A2052A30 secondary: 52A3952A41star setstar bodydual mixed volumedual Brunn-Minkowski theoryconvex bodymixed volumeBrunn-Minkowski theorypositive functionaladditive functional 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. Indiana University Mathematics Journal 2016 text pdf 10.1512/iumj.2016.65.5765 10.1512/iumj.2016.65.5765 en Indiana Univ. Math. J. 65 (2016) 69 - 91 state-of-the-art mathematics http://iumj.org/access/