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Sankhya A

, Volume 72, Issue 1, pp 37–63 | Cite as

Big Vee: The story of a function, an algorithm, and three mathematical worlds

  • R. Purves
  • W. Sudderth
Article

Abstract

The Dubins-Savage theory of gambling takes place in a world of finitely additive probability measures defined on all subsets of a set of arbitrary cardinality. When the theory is specialized to a more conventional world of countably additive measures defined on the Borel subsets of a standard Borel space, the question arises whether the gambler is harmed when restricted to measurable strategies; that is, whether the optimal reward function V remains the same. The answer to this question uses methods from the world of descriptive set theory. Ashok Maitra was perhaps the unique person who was completely at home in all three of these mathematical worlds.

Keywords and phrases

Gambling house finite additivity Borel set analytic set inductive definability stochastic game 

AMS (2000) subject classification

Primary 60G40, 91A60, 93E20, 54H05, 03D70, 28A12, 28A20 

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Copyright information

© Indian Statistical Institute 2010

Authors and Affiliations

  1. 1.University of CaliforniaBerkeleyUSA
  2. 2.University of MinnesotaMinneapolisUSA
  3. 3.Department of StatisticsUniversity of CaliforniaBerkeleyUSA
  4. 4.School of StatisticsUniversity of MinnesotaMinneapolisUSA

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