## 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.## References

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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