This is an announcement for the paper "Characterizing the dual mixed volume via additive functionals" by Paolo Dulio, Richard J. Gardner and Carla Peri. Abstract: 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. Archive classification: math.FA math.MG Mathematics Subject Classification: Primary: 52A20, 52A30, secondary: 52A39, 52A41 Submitted from: Richard.Gardner@wwu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1312.4072 or http://arXiv.org/abs/1312.4072