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Proceedings of the American Mathematical Society

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

 

 

Nonexistence of measurable optimal selections


Authors: John Burgess and Ashok Maitra
Journal: Proc. Amer. Math. Soc. 116 (1992), 1101-1106
MSC: Primary 28B20; Secondary 54C65, 90C39
DOI: https://doi.org/10.1090/S0002-9939-1992-1120505-3
MathSciNet review: 1120505
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Abstract: We give an example of a function $ f$ on a separable metric space $ X$ into a compact metric space $ Y$ such that the graph of $ f$ is a Borel subset of $ X \times Y$, but $ f$ is not Borel measurable. The example forms the basis for our construction of an upper semicontinuous, compact model of a one-day dynamic programming problem where the player has an optimal action at each state, but is unable to make a choice of such an action in a Borel measurable manner.


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DOI: https://doi.org/10.1090/S0002-9939-1992-1120505-3
Keywords: Measurable selections, Borel sets and functions, dynamic programming
Article copyright: © Copyright 1992 American Mathematical Society