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A generalization of Lyapunov's convexity theorem with applications in optimal stopping

Authors:	Zuzana Kü hn Uwe Rö sler

Institution:	School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332 ; Mathematisches Seminar der CAU Kiel, Christian-Albrechts-Universität zu Kiel, Ludewig-Meyn-Str. 4, 24098 Kiel, Germany

Abstract:	Lyapunov proved that the range of finite measures defined on the same $\sigma$ -algebra is compact, and if each measure $\mu _{i}$ also is atomless, then the range is convex. Although both conclusions may fail for measures on different $\sigma$ -algebras of the same set, they do hold if the $\sigma$ -algebras are nested, which is exactly the setting of classical optimal stopping theory.

Keywords:	Vector measure range optimal stopping

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