We give an alternative proof to the well known fact that each convex compact centrally symmetric subset of R-2 containing the origin is a zonoid, i.e., the range of a two dimensional vector measure, and we prove that a two dimensional zonoid whose boundary contains the origin is strictly convex if and only if it is the range of a Chebyshev measure. We give a condition under which a two dimensional vector measure admits a decomposition as the difference of two Chebyshev measures, a necessary condition on the density function for the strict convexity of the range of a measure and a characterization of two dimensional Chebyshev measures. (C) 1997 Academic Press.
Two dimensional zonoids and Chebyshev measures
MARICONDA, CARLO
1997
Abstract
We give an alternative proof to the well known fact that each convex compact centrally symmetric subset of R-2 containing the origin is a zonoid, i.e., the range of a two dimensional vector measure, and we prove that a two dimensional zonoid whose boundary contains the origin is strictly convex if and only if it is the range of a Chebyshev measure. We give a condition under which a two dimensional vector measure admits a decomposition as the difference of two Chebyshev measures, a necessary condition on the density function for the strict convexity of the range of a measure and a characterization of two dimensional Chebyshev measures. (C) 1997 Academic Press.File | Dimensione | Formato | |
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