Characterizing the Dual Mixed Volume via Additive Functionals
نویسندگان
چکیده
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 BrunnMinkowski theory, obtained recently by Milman and Schneider, but the methods employed are completely different.
منابع مشابه
Translative and kinematic integral formulae concerning the convex hull operation
exists and can be expressed in terms of K and K ′. The functionals F under consideration are derived from the mixed volume or the mixed area measure functional. Analogous questions are treated for the motion group instead of the translation group. The resulting relations can be regarded as dual counterparts to various versions of the principal kinematic formula. Motivation for our investigation...
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