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As a generalization of the notion of measure, valuations have long played a central role in the integral geometry of convex sets. In recent years there has been a series of striking developments. Several examples were presented at this meeting, e.g. the work of Bernig and Fu on the integral geometry of groups acting transitively on the unit sphere, that of Hug and Schneider on kinematic and Crofton formulas for tensor valued valuations and a series of results by Ludwig and Reitzner on classifications of affine invariant notions of surface areas and of convex body valued valuations.
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Semyon Alesker, Andreas Bernig, Peter Schuster, Mini-Workshop: Valuations and Integral Geometry. Oberwolfach Rep. 7 (2010), no. 1, pp. 141–178DOI 10.4171/OWR/2010/04