11.07.2015 Views

International Congress of Mathematicians

International Congress of Mathematicians

International Congress of Mathematicians

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760 Semyon Alesker2. Translation invariant continuous valuationsFor a linear finite dimensional real vector space V let us denote by Val(V) thespace <strong>of</strong> translation invariant continuous valuations on V. This is a Fréchet spacewith respect to the topology <strong>of</strong> uniform convergence on compact subsets <strong>of</strong> /C(V).In this section we will discuss properties <strong>of</strong> this space.2.1. Irreducibility theorem and Poincaré dualityIt was shown by P. McMullen [17] that the space Val(V) <strong>of</strong> translation invariantcontinuous valuations on V has a natural grading given by the degree <strong>of</strong>homogeneity <strong>of</strong> valuations. Let us formulate this more precisely.2.1.1 Definition. A valuation 0

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