GEOMETRY OF THE RANGE OF A VECTOR MEASURE
Keywords:
Convex function, geometry of the range of a measure pair, the lower and upper bounds of the range, degree of non-convexity, cumulative distribution function, right expanding measure.
Abstract
A.A. Lyapunov [18] in 1940 proved that the range of a countably additive bounded measure with values in a finite dimensional vector space is compact and, in the non-atomic case, is convex. Simplified proofs, unified versions, topological versions, generalizations and related theory have appeared in literature from time to time and recently in a series of papers by D. E. Wulbert, for instance, [21]. [16] gives a comprehensive critical survey. In this paper the range of a two dimensional vector measure with emphasis on geometry, particularly, its boundary is studied
Published
2020-03-02
Section
Articles