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Article | REF: AF220 V1

Convex Geometry II. Distances and Measures, Approximation, Comparison and Symmetrisation

Author: Jean-Charles PINOLI

Publication date: November 10, 2020

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6. Intrinsic volumes in...

CI above: Intrinsic volumes in ℝ2n

The sizes of convex bodies at ℝ2n (volumes, surface perimeters and areas, diameters, etc.) can be referred to as intrinsic volumes.

6.1 Volumes

Historically, the volume of a convex body was defined by approximations by polytope volumes (in dimension 2 by D. Hilbert (1899), then in dimension 3 by H. Minkowski (1911) (p. 46 of

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