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SATURATED STRUCTURES FROM PROBABILITY THEORY
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 Title & Authors
SATURATED STRUCTURES FROM PROBABILITY THEORY
Song, Shichang;
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 Abstract
In the setting of continuous logic, we study atomless probability spaces and atomless random variable structures. We characterize -saturated atomless probability spaces and -saturated atomless random variable structures for every infinite cardinal . Moreover, -saturated and strongly -homogeneous atomless probability spaces and -saturated and strongly -homogeneous atomless random variable structures are characterized for every infinite cardinal . For atomless probability spaces, we prove that -saturation is equivalent to Hoover-Keisler saturation. For atomless random variable structures whose underlying probability spaces are Hoover-Keisler saturated, we prove several equivalent conditions.
 Keywords
continuous logic;saturation;Maharam spectrum;probability algebras;random variables;
 Language
English
 Cited by
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