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A Generalization of Lyapounov's Convexity Theorem to Measures with Atoms
Proceedings of the American Mathematical Society
  • John Elton, Georgia Institute of Technology - Main Campus
  • Theodore P. Hill, Georgia Institute of Technology - Main Campus
Publication Date
2-1-1987
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 α n/2, where α is the largest (one-dimensional) mass of the atoms of the measure. The case α = 0 yields Lyapounov's Convexity Theorem; applications are given to the bisection problem and to the bang-bang principle of optimal control theory.
Disciplines
Citation Information
John Elton and Theodore P. Hill. "A Generalization of Lyapounov's Convexity Theorem to Measures with Atoms" Proceedings of the American Mathematical Society Vol. 99 Iss. 2 (1987) p. 297 - 304
Available at: http://works.bepress.com/tphill/33/