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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Authors: Zuzana Kühn and Uwe Rösler
Journal: Proc. Amer. Math. Soc. 126 (1998), 769-777
MSC (1991): Primary 28B05; Secondary 60G40
MathSciNet review: 1423312
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Abstract: Lyapunov proved that the range of $n$ 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.


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Additional Information

Zuzana Kühn
Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332
Address at time of publication: Brinkmannstr. 4, 12169 Berlin, Bermany
Email: gt9843a@prism.gatech.edu

Uwe Rösler
Affiliation: Mathematisches Seminar der CAU Kiel, Christian-Albrechts-Universität zu Kiel, Ludewig-Meyn-Str. 4, 24098 Kiel, Germany
Email: nms34@rz.uni-kiel.d400.de

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04120-3
PII: S 0002-9939(98)04120-3
Keywords: Vector measure, range, optimal stopping
Received by editor(s): February 26, 1996
Received by editor(s) in revised form: September 3, 1996
Communicated by: Stanley Sawyer
Article copyright: © Copyright 1998 American Mathematical Society