# Purification, saturation and the exact law of large numbers

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## Abstract

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.

## Keywords

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

C60 C70## Preview

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