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Das gemischte Volumen als Distribution

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Abstract

It is shown that there exists a distribution T on Ωn (Ω unit sphere of Euclidean n-space) such that the mixed volume V(K1,...,Kn) equals\(T(H_{K_1 } \otimes \cdots \otimes H_{K_n } )\)for all convex bodies Ki, where\(H_{K_i } \) is the support function of ki and ⊗ denotes the tensor product. As a consequence, mixed volumes are approximated uniformly by n-fold integrals of the corresponding support functions.

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  1. Mathematisches Institut II, Universität Karlsruhe, Englerstr. 2, D-7500, Karlsruhe

    Wolfgang Weil

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  1. Wolfgang Weil
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Weil, W. Das gemischte Volumen als Distribution. Manuscripta Math 36, 1–18 (1981). https://doi.org/10.1007/BF01174809

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