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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A generalization of Lyapounov’s convexity theorem to measures with atoms
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by John Elton and Theodore P. Hill PDF
Proc. Amer. Math. Soc. 99 (1987), 297-304 Request permission

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.
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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 99 (1987), 297-304
  • MSC: Primary 28B05; Secondary 46G10, 49B36, 60A10
  • DOI: https://doi.org/10.1090/S0002-9939-1987-0870789-X
  • MathSciNet review: 870789