We give an alternative proof to the well known fact that each convex compact centrally symmetric subset of R2 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.
Two dimensional zonoids and Chebyshev measures / Bianchini, S.; Mariconda, C.; Cerf, R.. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - 211:2(1997), pp. 512-526. [10.1006/jmaa.1997.5486]
Two dimensional zonoids and Chebyshev measures
Bianchini, S.;
1997-01-01
Abstract
We give an alternative proof to the well known fact that each convex compact centrally symmetric subset of R2 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.File | Dimensione | Formato | |
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