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 | References | Similar Articles | Additional Information

Abstract: We give an example of a function on a separable metric space into a compact metric space such that the graph of is a Borel subset of , but 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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Additional Information

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