Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A generalization of Lyapounov's convexity theorem to measures with atoms


Authors: John Elton and Theodore P. Hill
Journal: Proc. Amer. Math. Soc. 99 (1987), 297-304
MSC: Primary 28B05; Secondary 46G10, 49B36, 60A10
MathSciNet review: 870789
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The distance from the convex hull of the range of an $ n$-dimensional vector-valued measure to the range of that measure is no more than $ \alpha n/2$, where $ \alpha $ is the largest (one-dimensional) mass of the atoms of the measure. The case $ \alpha = 0$ yields Lyapounov's Convexity Theorem; applications are given to the bisection problem and to the bang-bang principle of optimal control theory.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 28B05, 46G10, 49B36, 60A10

Retrieve articles in all journals with MSC: 28B05, 46G10, 49B36, 60A10


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0870789-X
PII: S 0002-9939(1987)0870789-X
Keywords: Range of a vector measure, convexity theorem, vector measures with atoms, dent-size of a nonconvex set, zonotope, zonohedron
Article copyright: © Copyright 1987 American Mathematical Society