On a Generalization of Lyapounov's Theorem
نویسندگان
چکیده
We provide a simpler proof of Gouweleeuw’s theorem about the convexity of the range of an R-valued vector measure Fin terms of $. We also discuss possible extensions of Gouweleeuw’s results to vector measures with values in infinite-dimensional vector spaces and to unbounded vector measures.
منابع مشابه
A Generalization of Lyapounov's Convexity Theorem to Measures with Atoms
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 an/2, where a is the largest (one-dimensional) mass of the atoms of the measure. The case a = 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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تاریخ انتشار 2003