Economic Theory

, Volume 50, Issue 3, pp 527–545 | Cite as

Purification, saturation and the exact law of large numbers

Research Article


Purification results are important in game theory and statistical decision theory. We prove a new purification theorem that generalizes several earlier results. The key idea of our proof is to make use of the exact law of large numbers. As an application, we show that every mixed strategy in games with finite players, general action spaces and diffused, conditionally independent incomplete information has many strong purifications.


Exact law of large numbers Fubini extension Incomplete information Purification Saturated probability space 

JEL Classification

C60 C70 


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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Science and Technology of ChinaHefeiPeople’s Republic of China
  2. 2.Department of MathematicsNational University of SingaporeSingaporeSingapore
  3. 3.Hausdorff Research Institute for MathematicsBonnGermany

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