SATURATED STRUCTURES FROM PROBABILITY THEORY

Title & Authors
SATURATED STRUCTURES FROM PROBABILITY THEORY
Song, Shichang;

Abstract
In the setting of continuous logic, we study atomless probability spaces and atomless random variable structures. We characterize $\small{{\kappa}}$-saturated atomless probability spaces and $\small{{\kappa}}$-saturated atomless random variable structures for every infinite cardinal $\small{{\kappa}}$. Moreover, $\small{{\kappa}}$-saturated and strongly $\small{{\kappa}}$-homogeneous atomless probability spaces and $\small{{\kappa}}$-saturated and strongly $\small{{\kappa}}$-homogeneous atomless random variable structures are characterized for every infinite cardinal $\small{{\kappa}}$. For atomless probability spaces, we prove that $\small{{\aleph}_1}$-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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