The absence of atoms in Lyapunov's Convexity Theorem is a sufficient, but not a necessary condition for the convexity of the range of an n-dimensional vector memure. In this paper algebraic and topological convexity conditions generalizing Lyapunov's Theorem are developed which are sufficient and ne
✦ LIBER ✦
Characterization of the closed convex hull of the range of a vector-valued measure
✍ Scribed by Igor Kluvánek
- Publisher
- Elsevier Science
- Year
- 1976
- Tongue
- English
- Weight
- 772 KB
- Volume
- 21
- Category
- Article
- ISSN
- 0022-1236
No coin nor oath required. For personal study only.
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## Abstract We introduce the concept of radius of pointedness for a closed convex cone in a finite dimensional Hilbert space. Such radius measures the degree of pointedness of the cone: the bigger the radius, the higher its degree of pointedness. We also discuss the question of measuring the degree
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