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A Generalization of Lyapounov's Convexity Theorem to Measures with Atoms

John Elton and Theodore P. Hill
Proceedings of the American Mathematical Society
Vol. 99, No. 2 (Feb., 1987), pp. 297-304
DOI: 10.2307/2046629
Stable URL: http://www.jstor.org/stable/2046629
Page Count: 8
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A Generalization of Lyapounov's Convexity Theorem to Measures with Atoms
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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.

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