Hadwiger's characterization theorem classifies all continuous rigid motion invariant valuations on compact convex sets as consisting of the linear span of the elementary Minkowski mixed volumes (Quermassintegrals). In this paper a characterization theorem is given for the dual elementary mixed volumes, giving the analogue to Hadwiger's result for the dual Brunn-Minkowski theory of star-shaped sets. A classification is also given for continuous valuations satisfying such conditions as rotation invariance and homogeneity with respect to dilation.

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This paper has a sequel, Invariant valuations on star-shaped sets.